Two arrows are shot vertically upward. the second arrow is shot after the first one, but while the first is still on its way up. the initial speeds are such that both arrows reach their maximum heights at the same instant, although these heights are different. suppose that the initial speed of the first arrow is 31.8 m/s and that the second arrow is fired 1.82 s after the first. determine the initial speed of the second arrow.

Answers

Answer 1

Final answer:

To determine the initial speed of the second arrow when both arrows reach their maximum height at the same time, kinematic equations are utilized, taking into account the initial velocity of the first arrow, delay time before the second arrow is fired, and gravity's acceleration.

Explanation:

The problem given is a classic example of two-body motion in which two arrows are launched vertically with different initial velocities, and the challenge is to find the initial speed of the second arrow when both arrows reach their peak heights simultaneously. To solve this problem, we need to use the equations of kinematics for each arrow.

First, we find the time it takes for the first arrow to reach its maximum height using the initial speed and the acceleration due to gravity. The equation for this is derived from the kinematic equation v = u + at, where v is the final velocity (0 m/s at maximum height), u is the initial velocity (31.8 m/s), a is the acceleration (-9.8 m/s² directed downwards), and t is the time. Thus, the time, t, for the first arrow to reach its maximum height can be calculated as follows:

t = (v - u) / a

Knowing the time it takes for the first arrow to reach the maximum height, we can then calculate the initial speed of the second arrow, which is fired 1.82 s later. This involves adding the delay time to the time it took the first arrow to reach the maximum height and then using that total time to determine the initial speed of the second arrow using the kinematic equation u = v - at, with v again being 0 m/s at maximum height.

By carefully evaluating these kinematic equations, we find the initial speed of the second arrow, ensuring that both arrows reach their peak heights at the same moment.


Related Questions

A car is traveling at a constant speed of 23 m/s on a highway. at the instant this car passes an entrance ramp, a second car enters the highway from the ramp. the second car starts from rest and has a constant acceleration. what acceleration must it maintain, so that the two cars meet for the first time at the next exit, which is 3.0 km away?

Answers

23 m/s (dividing by 1000 m/km) = 0.023 km/sDistance (3 km) divided by Speed (0.023 km/s) gives us Time = 130.43478... secSo it takes the first car mentioned about 130 seconds to move from the entrance ramp to the next exit.
We would like the second car to cover the same distance in the same time, but not be traveling at a steady pace, instead start at 0 and constantly increase speed. Even though the speed will be changing each instant, the AVERAGE speed of the second car will be the same as the speed of the first car over those 3 km in order for them to meet again. So the average speed of the second car will be 23 m/s.
Acceleration is a rate of change of speed, (or average speed divided by time). So, to find the acceleration of the second car, we divide 23 m/s by the time 130.43... s. This yields 0.17633333... m/s^2 as the acceleration needed."

Final answer:

To catch up with the first car at the exit 3.0 km away, the second car, starting from rest, must maintain an acceleration of approximately 0.3524 m/s².

Explanation:

To solve for the acceleration that the second car must maintain to meet the first car at the next exit 3.0 km away, we can use the equations of motion for uniformly accelerated motion.

Since the first car is traveling at a constant speed of 23 m/s and the distance to the next exit is 3.0 km (which is 3000 meters), we can determine the time it will take for the first car to reach the exit. The time (t) can be found using the equation:

Distance = Speed × Time

So, for the first car, Time = Distance/Speed = 3000 m / 23 m/s = 130.43 seconds.

The second car starts from rest (initial velocity = 0) and must cover the same 3000 meters in the same time, but under constant acceleration. We can use the equation for displacement under constant acceleration:

Displacement = Initial Velocity × Time + (1/2) × Acceleration × Time²

Since the initial velocity (u) is 0 m/s for the second car, the equation simplifies to:

3000 m = (1/2) × Acceleration (a) × (130.43 s)²

Now we can solve for the acceleration (a):

Acceleration = (2 × 3000 m) / (130.43 s)²

Acceleration = 6000 m / 17022.1849 s²

Acceleration = 0.3524 m/s²

Therefore, the second car must maintain an acceleration of approximately 0.3524 m/s² to meet the first car at the exit.

In a movie, a character cuts a wire, which stops the countdown timer of a bomb. What does cutting the wire do to the circuit?
A.) It opens the circuit so that electric charges do not flow to the timer.
B.) It closes the circuit so that electric charges do not flow to the timer.
C.)It opens the circuit so that electric charges flow to the timer.
D.) It closes the circuit so that electric charges flow to the timer.

Answers

A.) It opens the circuit so that electric charges do not flow to the timer.

Explanation:

A circuit is said to be "closed" if all its points are connected, so that the  current can flow without interruption, while it is said to be "open" if the circuit is interrupted somewhere so that the current cannot flow through it.

In the movie, the character cuts the wire: this way, he opens the circuit, because the charges (the electons) that carry the current cannot flow through it anymore. Therefore, the correct choice is

A.) It opens the circuit so that electric charges do not flow to the timer.

Answer:

A.) It opens the circuit so that electric charges do not flow to the timer.

Explanation:

A child dangles a 1.50-kilogram stuffed toy 0.500 meters from the ground. What is the potential energy of the toy?
Answers are:
0.188 J
0.750 J
7.35 J
14.7 J

Answers

since we know that
Gravitational potential energy = mass × height ×gravity

then

GPE = 1.5 kg x 0.500 m x 9.8m/s^2

therefore

GPE = 7.35 J

Answer: 7.35 Joules

Explanation:

i got it right in my exam

When you double your speed, it takes about _____ times as much distance to stop?

Answers

4 times as much distance to stop

What is the weight on earth of a girl with a mass of 17 kg?

Answers

The gravity on earth is about 9.8 thus you times the mass by the gravity on earth:
17*9.8 = 166.6

Hope this helps! :)

A car is traveling with constant velocity. this means that _______.

Answers

It is traveling in a straight line and its speed is not changing

A car is traveling with constant velocity. this means that its position changes with time at constant rate at same direction.

What is velocity?

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.

Velocity informs us about the rate of change of your position, or how quickly your position changes per unit time. Velocity is described in physics as displacement divided by time, where displacement is the difference between your final and initial positions. Furthermore, an object is considered to be moving with constant velocity if it travels the same distance every second. This means that both the amount and direction of the velocity (or speed) stay constant.

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How does a roller coaster create the sensations of falling, and being thrown around?

Answers

I think when one gets to a certain height n a roller coaster the experience weightlessness. then, once the roller coaster starts shooting down, the feeling of gravity comes back to you. 

Final answer:

Roller coasters utilize physics principles like the conversion between potential and kinetic energy, and the manipulation of forces, to create sensations of falling and being thrown around. Apparent weightlessness and centrifugal forces are key in generating these feelings, providing riders with thrilling experiences through rapid descents and high-speed turns.

Explanation:

How Roller Coasters Create Sensations of Falling and Being Thrown Around

Roller coasters are engineered marvels that utilize basic physics principles to create thrilling experiences for riders. The sensations of falling and being thrown around are primarily caused by the manipulation of forces and energy. When a roller coaster car climbs up a hill, it is building potential energy, which is then converted into kinetic energy as it descends. This transition between potential and kinetic energy is what propels the car along the track at high speeds, over hills, and through loops.

Apparent weightlessness is experienced when the car rapidly descends, creating a feeling of free fall. This is similar to the sensation you might feel on a ride like the Supreme Scream, where riders are dropped from a height, causing their guts to feel like they're floating. This feeling is a result of the decreasing force of gravity acting on the riders as they accelerate downwards.

In other attractions, such as the vertical barrel ride, riders experience being pinned to the wall due to centrifugal force. While this force is fictitious in an inertial frame of reference (Earth), it is very real to those in the rotating frame of the ride. The real forces at play include the normal force exerted by the wall on the riders, which counters the gravitational force, creating the sensation of being pressed against the wall.

Roller coasters and similar rides cleverly utilize these principles to create the exhilarating experiences riders love, combining changes in speed, direction, and altitude to manipulate the forces acting on the body.

Which would hold more water- a teaspoon (tsp) or a milliliter?

Answers

A tsp

1 milliliter equals 0.202. US teaspoons. boi did that help

Answer:

A teaspoon

Explanation:

As we know that the capacity of hold something by a standard teaspoon is related with milliliters as,

1 teaspoon is equivalent to 4.92892 milliliters

From this it can be see that the 1 teaspoon is equivalent to approximately 5 milliliters.

Therefore, the water hold by 1 teaspoon is more than the water hold by a milliliter.

If 500 thousand btus of energy are available to raise the temperature of a water boiler from 20°f to 100°f, how many gallons of water can be added to the boiler?

Answers

Final answer:

If 500 thousand BTUs of energy are available to raise the temperature of a water boiler from 20°F to 100°F, then the amount of water that can be added to the boiler is 750 gallons.

Explanation:

The subject of this question is physics, specifically the application of thermodynamics in heating water. Given that 1 BTU is the amount of energy needed to heat one pound of water by one degree Fahrenheit, first we need to convert the weight of water from gallons to pounds (since 1 gallon of water weighs about 8.34 pounds). Then, if we are to increase the temperature of the water from 20°F to 100°F, that's a 80°F difference. Hence, the energy required to heat one pound of water from 20°F to 100°F is 80 BTU.

So, if there are 500 thousand BTUs available, the amount of water (in pounds) that can be heated will be 500,000 BTUs divided by 80 BTU per pound, equating to 6250 pounds. Converting this weight back to gallons (since 1 pound of water is approximately 0.12 gallons), the amount of water that can be added to the boiler is 750 gallons.

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Using 500,000 BTUs of energy, you can raise the temperature of approximately 781.25 gallons of water from 20°F to 100°F, given the specific heat capacity of water and its density. This calculation is based on the energy required to heat each pound of water and converting that to gallons.

To determine how many gallons of water can be heated from 20°F to 100°F using 500,000 BTUs of energy, we need to use the specific heat capacity of water. The specific heat capacity of water is 1 BTU per pound per degree Fahrenheit.

First, calculate the total temperature change:

ΔT = 100°F - 20°F = 80°F

Next, we use the formula:

Energy = mass * specific heat capacity * ΔT

Rearrange to solve for mass (in pounds):

mass = Energy / (specific heat capacity * ΔT)

Insert the known values:

mass = 500,000 BTU / (1 BTU/lb/°F * 80°F) = 6,250 pounds

Since the density of water is approximately 8 pounds per gallon, convert the mass of water to gallons:

gallons = mass / density = 6,250 pounds / 8 pounds/gallon = 781.25 gallons

So, you can add approximately 781.25 gallons of water to the boiler.

A fox is 7 meters from the base of a tree that is 15 m tall. A nest of owls is at the top of the tree. One of the owlets tosses a piece of meat horizontally from the nest at 1.2 m/s. The fox runs to catch the meat just before it hits the ground. What is the speed of the fox just as he catches the meat?

Answers

Refer to the diagram shown below.

In this analysis, wind resistance is ignored, and g = 9.8 m/s².

The meat falls with zero vertical velocity, therefore the time, t, before the meat hits the ground is
[tex] \frac{1}{2}*(9.8 \, \frac{m}{s^{2}})*(t \, s)^{2} = (15 \, m) \\ t= \sqrt{ \frac{15}{4.9} }= 1.75 \, s[/tex]

If the fox catches the meat before it hits the ground, then the fox should travel a horizontal distance d in the same time that the meat travels a horizontal distance (7 -d).
The meat travels a distance of 
7 - d = (1.2 m/s)*(1.75 s) = 2.1 m
or
d = 4.9 m

Let v =  velocity of the fox when it catches the meat.
If the acceleration of the fox is a m/s², then
v = 1.75a
Also,
[tex]d= \frac{1}{2} *(a \, \frac{m}{s^{2}} )*(1.75 \, s)^{2} = \frac{1}{2}( \frac{v}{1.75})^{2}*(1.75^{2}) \\ 4.9 = 0.875v^{2} \\ v^{2} = 5.6 \\ v = 2.366 \, m/s[/tex]

Answer:  2.37 m/s  (nearest hundredth)



What determines the direction that molecules move during diffusion?

Answers

the amount of energy that the molecule has 
Concentration Gradient. Passive diffusion = HIGH concentration to LOW concentration & Active diffusion = LOW to HIGH.

The physics explanation is "Electric Charge".

One of the advantages of solar energy is that it is _____.

Answers

The main advantage of solar energy is that it is a renewable source of energy.

This means that the energy obtained from the sun is always present as long as the sun exists and can never terminate (since the sun will always be present till the end of life on earth).

Energy from the sun is also a clean source of energy as it causes no pollution to the environment.

One of the advantages of solar energy is that it is nonpolluting. :)

Scientists are concerned about the release of methane from the arctic because _______. a. as a greenhouse gas methane is 20 times more potent than carbon dioxide b. the mass of the arctic’s methane is comparable to that of the Earth’s coal beds c. global warming appears to be accelerating its release d. all of the above

Answers

D: All of the above

I know methane is deadly and global warming is accelerating.

Answer: d. all of the above

Methane is a powerful greenhouse gas that contributes to the phenomena of global warming. One mole of methane is 10 times more powerful than one mole of CO₂. It is a dominant greenhouse gas. In Artic region the methane is released from the sea bed and the permafrost soil.  The methane is released as natural gas reserve from these sources as a outcome of the process of methanogeneisis. It involves the partial or uncomplete degradation of dead remains of animals and plants and rapid heating and thawing conditions.

The gas releases in the atmosphere because of all the four options.


You are building a canoe, and you want to make it out of metal. which property would be most important to consider in choosing which metal to use?

Answers

the density of the metal is important because if its more dense than water it will sink but if its lighter than water it will float

*PHYSICS HELP*

Without using your spring scale, estimate the order of magnitude of the mass of your calculator in grams from what you judge to be its size, using the fact that the density of water is 1 g/cm3. Assume that the density of water is about the same as the density of your calculator.
1 g 
102 g
104 g
106 g

Answers

We consider that my calculator has the following dimensions (approx) : Length = 14 cm Width = 7 cm Heigth= 2 cm Then the volum of the calculator will be V=Length x Width x Height = 196 cm3 If we assume that my calculator has the same density of water, that is 1 g/cm3 that means my calculator mass is: M = 196 cm3 * 1 g/cm3 = 196 grams

An airplane flies 12 m/s due north with a velocity of 35.11 m/s. how far east does it fly?

Answers

The plane's velocity of 35.11 m/s is actually due in a north-eastward direction. The 12 m/s velocity is the vertical component of the plane's velocity, hence it is pointing northwards. We will use the formula:

Vy = Vsin∅

To determine the angle ∅ at which the plane is flying. This is:

12 = 35.11 * sin∅
∅ = 20.0 degrees

The eastward velocity is:

Vx = Vcos∅
Vx = 35.11 * cos(20)
Vx = 33.0 m/s

The plane's eastward velocity is 33.0 m/s
The question says: The airplane flew due north for the given duration  (i interpret m/s to be milliseconds) and at the given velocity.

 The statement mentions no change in direction or angle, therefore the airplane does not fly east (or the airplane travels 0.0m east).

A spherical ball of lead has a diameter of 7.5 cm . what is the mass of the sphere if lead has a density of 11.34 g/cm3? (the volume of a sphere is (43)Ïr3 where r is the radius.)

Answers

Final answer:

To find the mass of the lead sphere, calculate its volume using the given diameter and the formula for the volume of a sphere. Then, use the density of lead to find the mass of the sphere.

Explanation:

To find the mass of the spherical ball of lead, we need to first find the volume of the sphere using the given diameter. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since the diameter is given as 7.5 cm, the radius is half of the diameter, which is 3.75 cm or 0.0375 m. We can now calculate the volume of the sphere:



V = (4/3)π(0.0375)^3 = 0.0223 m^3



Next, we can use the density of lead, which is given as 11.34 g/cm^3, to find the mass of the sphere. The density is the mass per unit volume, so we can set up the equation:



Mass = Density × Volume = 11.34 g/cm³ × 0.0223 m³ = 0.253 g



Therefore, the mass of the sphere of lead is 0.253 g.

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The push of air on earth is called

Answers

The answer is Air Pressure
The answer is air pressure
Air has a certain amount of mass from its molecules and because of earth's gravity forces, the air now has a certain amount of weight (weight = mass x gravity) Air pressure is created because of the weight of the air pushing down on the atmosphere and the surface below it.

Which of the following terms relate to one another?

a.fireplace, radiator
b.furnace, boiler
c.furnace, radiator
d.boiler, radiator

Answers

The correct answer is D.

Answer:

FURNACE & BOILER

Explanation:

The terms "furnace" and "boiler" relate to one another because they are both forms of central heating. A boiler uses hot water to heat a home, and a furnace uses warm air.

Is work done when you lift a brick?
A.No, the force applied is parallel to the direction of motion.
B.Yes, the force applied is parallel to the direction of motion.
C.No, the force applied is perpendicular to the direction of motion.
D.Yes, the force applied is perpendicular to the direction of motion.

Answers

it is B.

Yes, the force applied is parallel to the direction of motion

Answer:

The answer is: "Yes, the force applied is parallel to the direction of motion" Hope this helps :)

Explanation:

A farmer pulls on his obstinate mule with 250 N of force to the right. The ground exerts a reaction force to the mule’s resistance of 250 N to the left. What is the net force on the mule system? What is the mule’s acceleration?

Answers

0 net force it is exerting an equal and opposite force against the mule. And since the net force is 0 then the acceleration would be 0 too.

In a series circuit, when you add more resistance, what will happen to the amount of current?

Answers

the amount of current will increase since they are inversely proportional

It actually decreases because I just took a lesson review questions and first I put Increase but it said that was wrong and then I put decrease and it said that was the right answer so it decreases

Temperature cannot be considered a field since there are occasions where it is not possible to measure it with a thermometer. True or False?

Answers

The answer would be false

a boat is headed with a velocity of 18 meters/second toward the west with respect to the water in a river. if the river is flowing with a velocity of 2.5 meters/second in the same direction as the boat. what would be the magnitude of the boat’s velocity?

Answers

both the boat and swimmer are going in the same direction, west.
The net velocity the boat is traveling is then:
18 m/s + 2.5 m/s = 20.5 m/s

The magnitude is the hypotenuse of the components but there is only an x component so magnitude = 20.5 m/s

Answer: Hi!

You know that the boat has a velocity of 18m/s with respect to the water, and the water has a velocity of 2.5m/s.

Both velocities are in the same direction.

Now, if you are standing in the shore, you have a velocity of 0m/h, then you will see the boat moving with his velocity with respect to the water plus the velocity of the water:

this is V = 18 m/s + 2.5m/s = 20.5m/s

Where the addition is direct because both vectors are in the same direction.

An automobile with a mass of 1232 kg accelerates at a rate of 2 m/s² in the forward direction. What is the net force acting on the automobile? N

Answers

Based on Newton's second law:
Force = mass x acceleration

For this problem: we have the mass = 1232 kg and the acceleration = 2 m/s^2
So, just substitute with the givens in the above equation to calculate the force as follows:
Force = 1232 x 2 = 2464 Newtons

The packets of energy that light travels in are called

Answers

A packets of light energy is called a photons.

Carl measures the temperature of the water at different depths of the lake to see if there is a relationship.

Independent Variable:

Dependent Variable:

Answers

Independent variable - Water depth

The independent variable is something that is purposely changed in order to see the effects of change on the dependent variable. So since Carl wants to measure the temperature of water at different depths we will purposely change the depth of the water in order to observe how this would affect the temperature. 

Dependent variable - Temperature of the water 

The dependent variable is something that is dependent on the independent variable and is assumed to change as the independent variable changes. So we can determine that the temperature of the water is the independent variable as Carl expects it to change with the depth of the water. Another reason we can determine this is the dependent variable is because Carl can change the depth of the water measured but not the temperature of the water depths. 
Final answer:

In Carl's experiment, the independent variable is the depth of the lake, which is being manipulated. The dependent variable is the temperature of the water, which may change based on the depth of measurement.

Explanation:

In this lake temperature measurement experiment, the independent variable is the depth of the lake. This is because Carl is manipulating or changing the depth where he is taking water temperature measurements. The dependent variable, on the other hand, is the temperature of the water. The temperature is dependent because its value can possibly change based on the depth of the lake where the temperature measurement is taken.

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What is the energy (in joules) of an ultraviolet photon with wavelength 110 nm?

Answers

For light or ultraviolet, the formula for energy can be calculated using Planck’s equation. That is:

E =  h c / ʎ

where,

h is the Planck’s constant = 6.626 * 10^-34 m^2 kg / s

c is the speed of light = 3 * 10^8 m/s

ʎ is the wavelength of light = 110 nm = 110 x 10^-9 m

 

So calculating for energy E:

E = (6.626 * 10^-34 m^2 kg / s) * (3 * 10^8 m/s) / (110 x 10^-9 m)

E = 1.807 x 10^-18 J

Light and radio waves travel through a vacuum in a straight line at a speed of very nearly 3.00 ´ 108 m/s. How far is light year (the distance light travels in a year)?

Answers

We need to calculate the number of seconds in one year. time = (365 days) (24 hours/day) (3600 seconds/hour) time = 31536000 seconds We can calculate the distance that light travels in this many seconds. distance = speed x time distance = (3.00 x 10^8 m/s) (31536000 seconds) distance = 9.46 x 10^{15} meters A light year is 9.46 x 10^{15} meters

Final answer:

A light-year, which is the distance light travels in a year at a speed of 3.00 x 10^8 m/s, is approximately 9.46 x 10^15 meters or about 10 trillion kilometers. This measure is essential in astronomy for gauging the distances between celestial bodies.

Explanation:

How Far Is a Light-Year?

A light year is the distance that light, traveling at a speed of 3.00 × 108 m/s in a vacuum, covers in one year. To find the distance light travels in a year, you multiply its speed by the number of seconds in a year (31,536,000 seconds).

So, the calculation would be 3.00 × 108 m/s × 31,536,000 s/year = 9.46 × 1015 meters/year. Thus, a light-year is approximately 9.46 × 1015 meters or about 10 trillion kilometers.

This distance is used in astronomy to measure the vast distances between celestial bodies in the universe. Since light travels at this constant speed in a vacuum, it enables scientists to estimate how far away stars and galaxies are based on how long their light takes to reach us.

What is the energy of a rock that weighs 125 n that is sitting on top of a hill 301 m high?

Answers

The gravitational potential energy is:

PE = (125 n) * (9.81 m/s^2) * (301 m)

PE = 37,253 J

If the rock were to fall from the top of the hill, it would gain kinetic energy as it falls and its potential energy would be converted to kinetic energy. The total energy of the rock would remain constant, as energy is conserved.

What is gravitational potential energy?

The energy of an object that is sitting on top of a hill is called gravitational potential energy. Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is defined as the work required to move an object from a reference position to its current position against the force of gravity.

The formula for gravitational potential energy is:

PE = m * g * h

where PE is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity (9.81 m/s^2 on Earth), and h is the height of the object above the reference position. The unit of gravitational potential energy is typically the joule (J).

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