Answers
The cannonball takes approximately 4.40 seconds to hit the wall and strikes it at a height of around 157.15 meters.
Let's solve this step by step:
Step 1: Calculate the time of flight
To find how long it takes for the cannonball to hit the wall, we need to consider the horizontal motion.
Initial horizontal velocity ([tex]u_x[/tex]): 89 m/s * cos(40°)[tex]u_x[/tex] = 89 * 0.766[tex]u_x[/tex] ≈ 68.174 m/sDistance to the wall (d): 300 mTime of flight (t) = d / [tex]u_x[/tex]t = 300 / 68.174t ≈ 4.40 secondsSo, it takes approximately 4.40 seconds for the ball to hit the wall.
Step 2: Calculate the height at which the ball hits the wall
For vertical motion:
Initial vertical velocity ([tex]u_y[/tex]): 89 m/s * sin(40°)[tex]u_y = 89 \times 0.643[/tex][tex]u_y \approx 57.227\ m/s[/tex]Vertical displacement (y) after time t: [tex]y = u_y \times t - 0.5 \times g \times t^2[/tex] (where g is the acceleration due to gravity, approximately 9.8 m/s²)
[tex]y = 57.227 \times 4.40 - 0.5 \times 9.8 \times (4.40)^2[/tex][tex]y \approx 251.79 - 94.64[/tex][tex]y \approx 157.15 meters[/tex]Therefore, the ball hits the wall at a height of approximately 157.15 meters.
The complete question is as follows:
A cannon elevated at 40 degrees is fired at a wall 300 m away on level ground. The initial speed of the cannonball is 89 m/sec.
1) how long does it take for the ball to hit the wall?
2) at what hight does the ball hit the wall?
Related Questions
What part of earth systems interact to form a storm like this hurricane near Florida
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How many times longer than the length of one year is the age of the universe?
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A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. what is its percent uncertainty?
Answers
The percent uncertainty in this question refers to how much measured values could deviate from a standard or expected value. For this example, considering a good-quality measuring tape that can be off by 0.50cm over a distance of 20m, the percent uncertainty is calculated as 0.0025%
Explanation:The concept this question is referring to is percent uncertainty, which is a quantitative measure of how much measured values deviate from a standard or expected value. It's widely used in physics and engineering. In a practical context, when you're using a measuring tape, it's unlikely you'll get a perfect measurement every time. This could be due to factors like the smallest division on the tape or the person using it having bad eyesight. In this particular example, measuring tape error was 0.50 cm over a distance of 20 m (or 2000 cm).
The percent uncertainty is calculated by dividing the uncertainty (the amount the measurement could be off by) by the measured value, and then multiplying by 100% to express it as a percentage.
So, percent uncertainty = (uncertainty/measured value) * 100%.
For this scenario, percent uncertainty = (0.50 cm / 20000 cm) * 100% which equals to 0.0025%.
So, in this example, the percent uncertainty is 0.0025%.
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The percent uncertainty of the measuring tape is 0.025%.
To find the percent uncertainty of a measurement, you use the following formula:
[tex]\text{Percent Uncertainty} = \left( \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \right) \times 100 \%[/tex]
Given:
Absolute Uncertainty = 0.50 cmMeasured Value = 20 metersFirst, convert the Measured Value to centimeters because the absolute uncertainty is given in centimeters.
[tex]20 \text{ m} = 2000 \text{ cm}[/tex]
Now, plug the values into the formula:
[tex]\text{Percent Uncertainty} = \left( \frac{0.50 \text{ cm}}{2000 \text{ cm}} \right) \times 100 \%[/tex]
Calculate the result:
[tex]\text{Percent Uncertainty} = \left( \frac{0.50}{2000} \right) \times 100 \% = 0.025 \%[/tex]
When the temperature is cold, Tim's tires look under-inflated. This is because the air molecules in the tire ________ causing their kinetic energy to _________ and volume to _______. A) slow down, decrease, contract B) multiply, increase, fluctuates C) stay the same, increase, expand D) speed up, decrease, stay the same
Answers
During cold times, air molecules speed up while the energy decreases. Since the volume stays the same, it appears as if the tires look under-inflated, while in reality they're not.
According to Newton’s first law of motion, what must happen to move an object at rest? It must move by its own inertia. It must gain potential energy. A force must act on it. Gravity must act on it.
Answers
a force must act on it
What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is w = 1.75 m wide and h = 8.00 m below the top of the cliff?
Answers
Final answer:
To avoid hitting the ledge when jumping from a cliff, calculate the time of flight using the height of the cliff and gravity, then use that time to find the minimum horizontal velocity needed to clear the ledge width.
Explanation:
Minimum Speed to Miss the Ledge
To find the minimum speed required for a person to miss the ledge when jumping from a cliff, one must analyze the motion in two dimensions: vertical and horizontal. The vertical distance (h) and the width of the ledge (w) are crucial to determine the time in the air and the minimum horizontal velocity needed.
The vertical motion is independent of the horizontal motion and can be analyzed using the formula for the time of flight under gravity which is t = [tex]\sqrt(2h/g)[/tex], where g is the acceleration due to gravity. Once the time of flight is calculated, we use this time to find the minimum horizontal velocity (vmin) necessary to travel the width of the ledge w by the formula vmin = w/t. This is the minimum speed the person needs just as they leave the edge of the cliff.
For a ledge 1.75m wide and cliff 8.00m high, first, calculate the time of flight with t = [tex]\sqrt((2*8.00m)/9.81m/s2)[/tex]. Then, use this time to calculate the horizontal velocity with v min = 1.75m / t.
Which of these statements are true about scientific theories and laws?
Theories are untested.
Laws are untested.
Laws are often expressed as math formulas.
A law is the same as a theory.
Theories are not opinions.
Answers
Answer:
Theories are not opinions.
Explanation:
Theories are all of them tested, with the scientific method in order to be accepted or refuted, then Laws are tested and are observable by any means all around the globe, the only option that is actually correct would be that Theories are not opinions because they are scientific statements that can be tested.
Answer:
theories are not opinions
Explanation:
How might a theory relate to a model
Answers
Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.8 m/s2 for 4.6 seconds. It then continues at a constant speed for 9.2 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 257.71 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.
How far does the blue car travel before its breaks are applied to slow down?
Answers
For constant acceleration:
a = v,final - v,initial /t
d = v,initial*t + 1/2*at²
For constant velocity:
d = constant velocity*time
The solutions is as follows:
a = v,final - v,initial /t
3.8 = (v₁ - 0)/4.6 s
v₁ = 17.48 m/s
Total distance = d1 + d2 + d3
d1 = d = v,initial*t + 1/2*at²
d2 = constant velocity*time
Total distance = 0*(4.6) + 1/2*(3.8)(4.6)² + (17.48)(9.2) + d3= 257.71
d3 = 56.69 m
A comet near the sun whose orbit is _______________ would never be near the sun again
Answers
Riders on the power tower are launched skyward with an acceleration of 4g, after which they experience a period of free fall. what is a 60 kg rider's apparent weight during the launch?
Answers
During the launch, the person was accelerating against the gravity, therefore the equation we use in this case is:
F = m * (g + a)
where m is mass = 60 kg, g is gravity = 9.81 m/s^2, a is acceleration = 4 * g
therefore:
F = m * (g + 4 g)
F = m * 5 g
F = 60 kg * 5 * (9.81 m/s^2)
F = 2943 N
The apparent weight of a 60 kg rider during the launch of a power tower ride experiencing 4g of acceleration is 2940 N. This is calculated by adding the force due to the rider's weight and the force due to the ride's acceleration.
Explanation:To calculate the apparent weight of a rider during the launch, we need to consider the gravitational force (weight) and the additional force due to the 4g acceleration of the ride. The weight of the rider is calculated using the formula: Weight = Mass x Gravity, where mass is 60 kg and gravity is 9.8 m/s². This gives a weight of approximately 588 N (Newton).
The force due to the ride's acceleration is calculated using the formula: Force = Mass x Acceleration, where in this case acceleration is 4g or 4 x 9.8 m/s², which gives approximately 2352 N.
The apparent weight of the rider is therefore the sum of these two forces: 588 N + 2352 N = 2940 N.
So a 60 kg rider's apparent weight during the launch is 2940 N.
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When the molecules in a body move with increased speed, it's possible that the body will change from a
A. liquid to a solid.
B. gas to a liquid.
C. liquid to a gas.
D. gas to a solid.
Answers
Given that increased speed means increased kinetic energy, the only possible solution is C because it is the only one which shows increased kinetic energy. The other options would be decreased, which means they are incorrect.
A cylindrical tube 14.0 cm high and 2.5 cm in diameter is used to collect blood samples. how many cubic decimeters (dm3) of blood can it hold (v of a cylinder = r2h)?
Answers
The formula to measure the volume of cylinder is V = h(r^2), where v = volume, r = radius, and h = height.
First, we plug those numbers into the formula. Remember that radius is one half of the diameter.
V = 14(2.5/2)^2
Simplify the problem.
V = 21.875
Now, let's convert this answer from centimeters to decimeters.
Since a decimeter is one tenth of a meter, we can divide the answer by ten.
= 21.875/10
Therefore, your answer is 2.1875dm3
A projectile is fired in such a way that its horizontal range is equal to 14.5 times its maximum height. what is the angle of projection?
Answers
The maximum height is:
hmax = v0² sin² α / 2 g
The horizontal range is: x = v0² sin 2 α / g
So we are given that:
x = 14.5 hmax
v0² sin 2 α / g
= 14.5 v0² sin² α / 2 g
7.25 sin² α = 2 sin α cos α
7.25 sin α = 2 cos α
7.25 tan α = 2
tan α = 0.27586
α = tan^(-1) 0.27586
α = 15.42°
The angle of projection is 15.42°
Objects A and B are brought close to each other. Object A will soon become positively charged. Identify the charge that must transfer for this situation to occur.
Answers
The following situation occurs:
The two objects are brought close to each other (but they do not touch). Object B must be negatively charged: in this case, for induction, the positive charges on object A migrate towards the side of the object closer to object B, while the negative charges migrate to the other side. Then, object A must be connected to the ground, so that the negative charges migrate to the ground: therefore, an excess of positive charges remain on object A, which is now positively charged.
Answer:
a positive charge will transfer from object b
Explanation:
a positive charge will transfer from object b to object a making a positively charged
Have a good day = )
You replace a 40 W incandescent lightbulb with an 8 W LED bulb. If you leave your lights on 24 hours a day, how much energy are you saving each day by replacing this bulb?
Answers
By replacing a 40 W incandescent bulb with an 8 W LED bulb and leaving the lights on for 24 hours, you would be saving 768 Wh of energy per day.
Explanation:The question is asking how much energy you can save by switching from a 40 W incandescent lightbulb to an 8 W LED bulb. The energy use of a bulb is determined by its power (wattage) and the time it is turned on. To calculate the energy saved, we need to compare the energy use of the two different bulbs, when they are turned on for the same time.
Step 1: We start by calculating the daily energy consumption of the 40 W incandescent light bulb. Energy (E) in watt-hours (Wh) can be calculated using the formula E = P*t, where P is the power in watts (W) and t is the time in hours. Therefore, for the 40 W incandescent bulb used 24 hours a day: E1 = 40 W * 24 hours = 960 Wh/day.
Step 2: Then we calculate the daily energy consumption of the 8 W LED bulb. For the LED bulb: E2 = 8 W * 24 hours = 192 Wh/day.
Step 3: To find the daily amount of energy saved, we subtract the energy use of the LED bulb from the energy use of the incandescent bulb: E saved = E1 - E2 = 960 Wh/day - 192 Wh/day = 768 Wh/day. Therefore, by replacing a 40 W incandescent lightbulb with an 8 W LED bulb and leaving the lights on for 24 hours a day, you can save 768 Wh of energy each day.
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_____ bias describes when your likes and dislikes affect how you think about something.
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A dynamite blast at a quarry launches a rock straight upward, and 2.4 s later it is rising at a rate of 10 m/s. assuming air resistance has no effect on the rock, calculate its speed (a) at launch and (b) 5.1 s after launch.
Answers
Answer:
(a) 33.52 m/s
(b) 16.46 m/s downward
Explanation:
Part (a)To find the initial speed of the rocket, we can use the kinematic equation:
[tex]v = u + at[/tex]
where:
u is the initial velocity of the object. v is the final velocity of the object.a is the constant acceleration of the object. t is the time elapsed during the acceleration.In this case:
v = 10 m/sa = -9.8 m/s²t = 2.4 sTherefore:
[tex]10 = u + (-9.8)(2.4)[/tex]
[tex]10 = u - 23.52[/tex]
[tex]u = 10 + 23.52[/tex]
[tex]u = 33.52 \textsf{ m/s}[/tex]
So, the speed of the rock at launch is 33.52 m/s.
Part (b)We can use the same kinematic equation to find the speed at t = 5.1 s:
[tex]v = u + at[/tex]
[tex]v = 33.52 + (-9.8)(5.1)[/tex]
[tex]v = 33.52 - 49.98[/tex]
[tex]v = -16.46 \textsf{ m/s}[/tex]
The negative sign indicates that the rock is moving downward at this time.
So, 5.1 seconds after launch, the speed of the rock is 16.46 m/s downward.
Consider a box sitting in the back of a pickup. The pickup accelerates to the right, and because the bed of the pickup is sticky, the box does not slide around the truck when this happens.What direction is the force acting on the box due to the truck?
Answers
Considering a box sitting in the back of a pickup. The pickup accelerates to the right, and because the bed of the pickup is sticky, the box does not slide around the truck when this happens. But the force acting on the box is left.
What is Force ?Force is responsible for the motion of an object. it produces acceleration in the body. According to newton's second law force is mass times acceleration i.e. F =ma. Its SI unit is N which is equivalent to kg.m/s².
There are two types of forces, balanced force and unbalanced force.
When Net force acting on a body is zero then we call it as balanced force. .
Unbalanced forces are those when resultant of all the forces is not equal to zero is called as unbalanced force. unbalanced force is responsible for the motion of the body.
Whatever we are talking about force in this problem is called as pseudo force, it same as we feel in the bus when we are standing in the bus suddenly driver brakes we go ahead in the bus or we feel forward force.
Pseudo force is not actual force but it can felt, centrifugal force is a type of pseudo force.
In this problem, as pickup accelerates, according to newtons first law box in the pickup tend to have its original velocity(0 if pickup is at rest or v when it is in motion). because of this when pickup accelerates right, box feel pseudo force in the opposite direction(Left).
Hence left is correct.
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Suppose the shipping company were packing balls with a diameter of 2 inches instead of Cubes. Would the large box hold more balls or fewer balls than boxes? Explain your answer.
Answers
Volume of cube = (edge)³ = (2 in)³ = 8 in³
Volume of sphere = (4πr³)/3
where r is the radius and is equal to half of the length of the sides. Substituting,
Volume of sphere = (4π)(1 in)³ / 3 = 4.19 in³
Since spheres give the smaller value for volume, the answer to this item would have to be SPHERE.
A particular baseball pitcher throws a baseball at a speed of 39.1 m/s (about 87.5 mi/hr) toward home plate. We use g = 9.8 m/s2 and ignore air friction.
(a) Assuming the pitcher releases the ball 16.6 m from home plate and throws it so the ball is initially moving horizontally, how long does it take the ball to reach home plate?
Answers
Three deer, a, b, and c, are grazing in a field. deer b is located 64.9 m from deer a at an angle of 53.4 ° north of west. deer c is located 77.9 ° north of east relative to deer
a. the distance between deer b and c is 96.8 m. what is the distance between deer a and c
Answers
Final answer:
Explanation of calculating the distance between two deer in a field using trigonometry and the Pythagorean theorem.
Explanation:
Given information:
Deer b is 64.9 m from deer a at an angle of 53.4° north of west. Deer c is 77.9 m north of east relative to deer a. The distance between deer b and c is 96.8 m.
To find: Distance between deer a and c.
Calculation:
Using trigonometry, we can find the distances and then apply the Pythagorean theorem to calculate the distance between deer a and c.
Distance between deer a and c is approximately 59.2 meters.
A car accelerates from 13-m/s to 24.1-m/s in 5.4-s. what was its acceleration in m/s2?
Answers
Then you divide the change in velocity by the time it took to change to find the acceleration.
11.1m/s÷5.4s =2.056 m/s^2
A truck covers 40.0 m in 8.50 s while smoothly slowing down to a final speed of 2.80 m/s. (a) find its original speed. (b) find its acceleration.
Answers
speed = 40.0m / 8.50s
speed = 4.71 m/s
acceleration equation: acceleration = change in velocity/time
4.71 - 2.80 = 1.91 (change in velocity)
acceleration = 1.91/8.50
acceleration = .22 m/s^2
a) 4.71 m/s
b) .22 m/s^2
Answer:
For a: The original speed of the truck is 4.76 m/s
For b: The acceleration of the truck is [tex]-0.23m/s^2[/tex]
Explanation:
For a:Speed is defined as the rate at which an object moves with respect to time.
To calculate the time taken for the given speed, we use the equation:
[tex]s=\frac{d}{t}[/tex]
where,
s = speed of the truck
d = distance traveled = 40.0 m
t = time taken by truck = 8.50 s
Putting values in above equation, we get:
[tex]s=\frac{40.0m}{8.50s}=4.76m/s[/tex]
Hence, the original speed of the truck is 4.76 m/s
For 2:Acceleration is defined as the rate of change of velocity with respect to time.
Mathematically,
[tex]a=\frac{v-u}{t}[/tex]
where,
v = final velocity of the truck = 2.80 m/s
u = initial velocity of the truck = 4.76 m/s
t = time taken = 8.50 s
Putting values in above equation, we get:
[tex]a=\frac{2.80-4.76}{8.50}=-0.23m/s^2[/tex]
Negative sign represents slowing down or deceleration.
Hence, the acceleration of the truck is [tex]-0.23m/s^2[/tex]
Fiora starts riding her bike at 20 mi/h. after a while, she slows down to 12 mi/h, and maintains that speed for the rest of the trip. the whole trip of 70 mi takes her 4.5 h. for what distance did she travel at 20 mi/h?
Answers
t = hours at 20 mi/hr
20t + 12*(4.5 - t) = 70
8t = 16
t = 2 hours
d at 20 mi/hr = 20*2 = 40 miles
40/20 + 30/12 = 4.5 hours
Fiora travels a total distance of 4.5 hours
Answer : Distance, d = 40 mi.
Explanation :
It is given that,
Fiora starts riding her bike at 20 mi/h. after a while, she slows down to 12 mi/h and maintains that speed for the rest of the trip. the whole trip of 70 mi takes her 4.5 h.
Let for t hours she traveled at 20 mi/h. So, for ( 4.5 - t) h she has traveled with a speed of 12 mi/h.
We know that,
distance covered = speed × time
20 mi/h × t +12 mi/h (4.5 h - t) = 70 mi
t = 2 h
So, the distance covered in 2 h is, d = 20 mi/h × 2 h = 40 mi.
Hence, this is the required solution.
A completely submerged object always displaces its own
Answers
Archimedes' principle states that a completely submerged object always displaces its own volume of water, creating an upward buoyant force.
Explanation:In physics, an object that is completely submerged underwater will always displace its own volume of water.
This is known as Archimedes' principle, which states that the buoyant force acting on an object is equal to the weight of the fluid it displaces.
For example, if a 1 liter object is submerged in water, it will displace 1 liter of water. This displacement results in an upward force, called the buoyant force, that opposes the weight of the object.
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A proton and an electron are separated by 6.5 Ã 10â10 m. (a) calculate the magnitude of the electric force that the proton exerts on the electron
Answers
8.99*10^9* ((charge of a proton*charge of an electron)/(6.5*10^10m)^2)
8.99*10^9* ((1.602*10^-19)(|-1.602*10^-19|)/((6.5*10^10)^2)
=5.4608*10^-50
We have that the magnitude of the electric force that the proton exerts on the electron
[tex]F=5.45*10^{-10}N[/tex]
From the question we are told that
proton and an electron are separated by 6.5 Ã 10â10 m
Generally the equation for the Force is mathematically given as
[tex]F=\frac{kq_1q_2}{r^2}\\\\F=\frac{9*10^{9}*(1.6*10^{-19})^2}{(6.5*10^{-10})^2}[/tex]
[tex]F=5.45*10^{-10}N[/tex]
Therefore
the magnitude of the electric force that the proton exerts on the electron
[tex]F=5.45*10^{-10}N[/tex]
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What is the chemical formula for mercury(I) nitrate? Hgmc021-1.jpg(NOmc021-2.jpg) Hg(NOmc021-3.jpg)mc021-4.jpg Hgmc021-5.jpg(NOmc021-6.jpg)mc021-7.jpg Hgmc021-8.jpg(NOmc021-9.jpg)mc021-10.jpg
Answers
Final answer:
The chemical formula for mercury(I) nitrate is Hg2(NO3)2, featuring a Hg₂²+ dimeric cation.
Explanation:
The chemical formula for mercury(I) nitrate is Hg2(NO3)2. This compound is created when a large excess of mercury reacts with dilute nitric acid. Mercury(I) compounds are unique because they contain a Hg₂²+ ion, which is a dimeric cation where two mercury atoms are bonded together, each with a +1 oxidation state, giving the overall molecule a +2 charge. It's important to note that the compound must be handled with care due to the toxicity of mercury compounds.
How many kilograms are there in a 2.00 L bottle of drinking water?
Answers
Jermaine runs exactly 2 laps arounda 400 meter track. What is his distance traveled?