A quarterback takes the football from the line of scrimmage and runs backward for 15 meters, he then runs sideways parallel to the line of scrimmage for 12 meters. At this point he throws the ball 50 meters perpendicular to the line of scrimmage where it is caught by the receiver. How far is the football from its original position?

Answer:

Option A and Option D are correct.

Explanation:

We have the Newton's second law, that is rate of change of momentum is force.

      [tex]\frac{dP}{dt}=F\\\\\frac{mv-mu}{dt}=F[/tex]

So if there is a force  mv - mu ≠ 0

                                 v - u ≠ 0

                                 v ≠ u

                     Final velocity ≠ Initial velocity.

  a) Option A is correct since there is a force

  b) Option B is wrong since total force is zero.

  c) Option C is wrong since total force is zero.

  d) Option D is correct since there is an effective force

Option A and Option D are correct.          

To find the x, y, and z components of the vector [tex]\(\vec{A}\)[/tex] shown in the diagram, we need to use trigonometric relationships.

Here are the steps to calculate each component:

Step 1: Understand the 3D vector components

- The vector [tex]\(\vec{A}\)[/tex] in a 3D space has three components, [tex]\(A_x\)[/tex] along the x-axis, [tex]\(A_y\)[/tex] along the y-axis, and [tex]\(A_z\)[/tex] along the z-axis.

- The given angles provide the direction of the vector in the 3D coordinate system.

Step 2: Calculate the z-component [tex](A_z)[/tex]

- Use the cosine of the angle between the vector [tex]\(\vec{A}\)[/tex] and the x-y plane, which is given as 35°. The cosine of this angle gives the ratio of the adjacent side [tex](A_z)[/tex] to the hypotenuse [tex](\(|\vec{A}|\))[/tex]:

[tex]\[ A_z = |\vec{A}| \cdot \cos(35°) \][/tex]

Step 3: Calculate the projection of A on the x-y plane [tex](A_xy)[/tex]

- Use the sine of the same angle to find the length of the projection of [tex]\(\vec{A}\)[/tex] on the x-y plane: [tex]\[ A_{xy} = |\vec{A}| \cdot \sin(35°) \][/tex]

Step 4: Calculate the x-component [tex](A_x)[/tex] and y-component [tex](A_y)[/tex]

- Now, use the projection [tex]\(A_{xy}\)[/tex] and the angle in the x-y plane (55°) to find [tex]\(A_x\)[/tex] and [tex]\(A_y\)[/tex]:

[tex]\[ A_x = A_{xy} \cdot \cos(55°) \][/tex]

[tex]\[ A_y = A_{xy} \cdot \sin(55°) \][/tex]

Step 5: Apply the calculations

- [tex]\(|\vec{A}| = 65 \, m\)[/tex], and we can now plug this value into the equations to calculate [tex]\(A_x\), \(A_y\), and \(A_z\).[/tex]

Let's perform these calculations.

The components of the vector [tex]\(\vec{A}\)[/tex] are approximately:

-[tex]\( A_x = 21.38 \)[/tex] m (along the x-axis),

- [tex]\( A_y = 30.54 \)[/tex]m (along the y-axis),

- [tex]\( A_z = 53.24 \)[/tex] m (along the z-axis).

To find the x, y, and z components of the vector a, we need more information about the vector. Without the direction or angles, we cannot determine the x, y, and z components of the vector a. Please provide more information so that we can help you further.

To find the x, y, and z components of the vector a, we need more information about the vector. From the given information, it seems that the magnitude of vector a is 65 m. However, the x, y, and z components of the vector require the direction or angles.

Without the direction or angles, we cannot determine the x, y, and z components of the vector a. Please provide more information so that we can help you further.

The acceleration of the car during [tex]4.0 s[/tex] is [tex]\boxed{-2.5\,{\text{m/}}{{\text{s}}^{\text{2}}}}[/tex] i.e. towards the west.

Further explanation:

Acceleration is caused due to the force exerted on the body. In case when body is in equilibrium, the net force on the body will be zero therefore, acceleration will also be zero.

In case when body is moving with certain initial velocity and the net force on the body is zero, body will continue to move with the same velocity or we can say body is moving with uniform velocity.

Given:

Initial velocity of the car is [tex]16\text{ m/s}[/tex] towards east.

Final velocity of the car is [tex]6\text{ m/s}[/tex] towards east.

Time interval is .[tex]4.0\text{ s}[/tex].

Concept:

Instantaneous acceleration is defined as the rate of change of velocity with respect to time. Average acceleration is defined as the change of velocity over a certain period of time.

Mathematically,

[tex]\boxed{a = \dfrac{{\Delta V}}{{\Delta t}}}[/tex]                 ……(1)

Here, [tex]a[/tex] is the average acceleration of car, [tex]\Delta V[/tex] is the change in velocity and [tex]\Delta t[/tex] is the time interval.

Write the expression for change in velocity

[tex]\Delta V = {V_{\text{f}}} - {V_{\text{i}}}[/tex]                       …… (2)

Here, [tex]{V_{\text{f}}}[/tex] is the final velocity of car and [tex]{V_{\text{i}}}[/tex] is the initial velocity of the car.

Velocity is a vector quantity so take magnitude as well as direction of the velocity, while substituting in the above expression.

Let’s assume unit vector in the east direction is [tex]\hat i[/tex] and unit vector in west direction is [tex]- \hat j[/tex].

Substitute [tex]6\,\hat i[/tex] for [tex]{V_{\text{f}}}[/tex] and [tex]16\,\hat i[/tex] for [tex]{V_{\text{i}}}[/tex] in equation (2).

[tex]\begin{aligned}\Delta V&=\left( {6{\kern 1pt} \hat i} \right) - \left( {16\,\hat i\,} \right)\\&=10\,\left( { - \hat i} \right)\\\end{aligned}[/tex]

Substitute [tex]10\,\left( { - \hat i} \right)[/tex] for [tex]\Delta V[/tex] and [tex]4.0\text{ s}[/tex] for [tex]\Delta t[/tex] in equation (1).

[tex]\begin{aligned}a&=\frac{{\left( { - 10\,\hat i\,{\text{m/s}}} \right)}}{{\left( {4.0\,{\text{s}}} \right)}} \\&=2.5\,\left( { - \hat i} \right)\,{\text{m/}}{{\text{s}}^{\text{2}}} \\ \end{aligned}[/tex]

Thus, the acceleration of the car during [tex]4.0 s[/tex] is [tex]\boxed{-2.5\,{\text{m/}}{{\text{s}}^{\text{2}}}}[/tex] i.e. towards the west.

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords:

Car, initial, velocity, 16.0 m/s, east, 16 m/s, 16 meter per second, 16.0 meter per second, uniformly, 6.0 m/s, 6 m/s, 6.0 meter per second, 6 meter per second, 4.0 second, 4.0 s, 4 second, 4 s, acceleration, during, interval.

The car decelerated at a rate of -2.5 m/s² east during the four-second interval.

The acceleration of a body can be calculated using the formula a = Δv/Δt, where 'a' is acceleration, 'Δv' is the change in velocity and 'Δt' is the change in time.

Here, the change in velocity (Δv) is the final velocity minus the initial velocity, hence Δv = 6.0 m/s - 16.0 m/s = -10.0 m/s. The change in time (Δt) is 4.0 seconds.

Plugging these values into our formula, we get a = -10.0 m/s / 4.0 s = -2.5 m/s².

The negative sign indicates that the car is decelerating or slowing down.

Therefore, the acceleration of the car during this 4.0 second interval is -2.5 m/s² east, meaning it is slowing down.

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To determine the magnitude of the initial acceleration of the 50-g particle, we can use the formula for the force between two charged particles and Newton's second law of motion.

To determine the magnitude of the initial acceleration of the 50-g particle, we can use the formula for the force between two charged particles and Newton's second law of motion. The force between two particles can be calculated using the equation F = k * (|q1 * q2| / r^2), where F is the force, k is Coulomb's constant (8.99 x 10^9 N*m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them. In this case, the force can be calculated as F = (8.99 x 10^9 N*m^2/C^2) * (5.0 mC * -20 mC) / (0.5 m)^2. Once we have the force, we can use Newton's second law of motion, F = m * a, to solve for the initial acceleration. Rearranging the equation, we find that a = F / m. Plugging in the values, we get a = (8.99 x 10^9 N*m^2/C^2) * (5.0 mC * -20 mC) / (0.5 m)^2 / 50 g. Calculating this value gives us the magnitude of the initial acceleration of the 50-g particle.

Saturn, Of the planets listed, Saturn is the greatest distance from the Sun. As a result, Saturn receives little of the Sun's warming energy and has a relatively cold surface temperature.

Answer:

The answer is C. Saturn

Explanation:

I had this question on stusdy lsland.

Answer: D) D

Explanation: According to the law of conservation of mass, mass can neither be created nor be destroyed. Thus the mass of products has to be equal to the mass of reactants. The number of atoms of each element has to be same on reactant and product side. Thus chemical equations are balanced.

As the atoms should remain conserved thus there should be 3 yellow atoms, three red atoms and 4 blue atoms in the products.

Thus the correct option is D.

The resulting mixture of the pair of enantiomers that is treated with a single enantiomer of another compound is the diastereomers which is in pair. The diastereomers usually happens when there is a mixture of stereoisomers but in terms of properties, they all have configurations that are different.

Answer: A. nerve cell groups to form tissue

Explanation: hope this helps

Answer:

Average velocity = [tex]\frac{1025}{13.5}  = 75.925 km/h[/tex].

Explanation:

To get the average velocity if the car traveled 1025 km in 13.5 hours means that you have to divide the km traveled by the hours:

Average velocity = [tex]\frac{1025}{13.5}  = 75.925 km/h[/tex].

The mass of a child of weight 300 N is calculated by dividing the weight by the standard acceleration due to gravity (9.8 m/s^2). Thus the child's mass is approximately 30.6 kg.

The weight of an object is the force of gravity on it and can be calculated by multiplying the mass of the object by the gravitational constant. The child's weight is given as 300 N. Based on the standard acceleration rate due to gravity, which is about 9.8 m/s2, we can find the mass using the formula W=mg where W is weight, m is mass, and g is gravity. Therefore, m=W/g which gives us m=300 N/9.8 m/s2 which is approximately 30.6 kg.

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C'est transféré à l'eau dans l'air à cause du

cycle de l'eau

The acceleration of the object is 2.8 [tex]m/s^2[/tex].

Given the following data:

To find the acceleration of the object:

Mathematically, acceleration is given by the formula;

[tex]A = \frac{V\; - \;U}{t}[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]A = \frac{36 \; - \;22}{5}\\\\A = \frac{14}{5}[/tex]

Acceleration, A = 2.8 [tex]m/s^2[/tex]

Therefore, the acceleration of the object is 2.8 [tex]m/s^2[/tex].

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Answer:

The answer is Force is equal to 25N

Explanation:

1) Taking into account Newton's second law, which expresses that the acceleration that a body acquires is directly proportional to that resulting from the forces acting on it, and has the same direction as that resulting.

2) This law is expressed with the formula F = ma where (F) represents force, (m) represents mass and (a) represents acceleration.

3) knowing this we can replace the values given in the problem and solve:

F = (0,5kg)(50m/s^2)

F = 25N

The spring experienced a contact force and the charge experienced a non-contact force.

If she stopped pulling no contact spring released.

No contact between charge and - charge, not necessarily, at least.

so i believe the correct answer is C)

Answer: C) bioluminescence

The middle layer of the world's ocean receives very little sunlight. This oceanic layer is called as twilight zone or diphotic zone or mesopelagic zone. This zone appears blue to black in color. The animals that live in this zone are adapted to survive in darkness, high pressure and cold water conditions.

The animals in this zone exhibit large eyes, which helps them to see in dark waters. Most animals are small, thin and dark which helps them to camouflage the predators in darkness. Some animals also possess large teeth and jaws. Many of these animals show bio luminescence, which means they can produce their own light. They have special organs which helps them to produce light by chemical reactions. Animals use light to find food and mates, they camouflage and distract the predators by light.

Answer:

C. Bio-luminescence

Explanation:

Twilight zones is also called meso-pelagic of diphotic zone. this is the zone in the ocean which receives very less sunlight so it appears blue or black in color.The animal which lives in this zone have adapted the capability to live under high pressure, in darkness and in low temperature so they have big eyes to watch the things in dark. Generally they are dark in color to camouflage the predators.

We have that a student walks 3 miles west and then 4 miles south to get to school the student displacement was

D=7miles

From the question we are told

a student walks 3 miles west and then 4 miles south to get to school the student displacement was

Generally the equation for the displacement  is mathematically given as

D=intial travel +final Travel

Therefore

D=3+4

D=7miles

Therefore

A student walks 3 miles west and then 4 miles south to get to school the student displacement was

D=7miles

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Explanation :  

Absorption coefficient of a material determines how much sound is absorbed by the material.

To build a soundproof room, Heavy curtains and carpet can be used. They reduce reverberation.

Reverberation means an echoing sound which persists for some time. For example, when we bang on a huge piece of metal, we hear the reverberation even after we stop banging.  

Hence, option (A) and (D) are correct.

Concrete, carpet, and heavy curtains would be the best materials to choose in order to absorb the most sound in a soundproof room.

If you were trying to build a soundproof room, concrete, carpet, and heavy curtains would be the best materials to choose in order to absorb the most sound, based on their coefficient of absorption.

Concrete is a dense and solid material that effectively absorbs sound waves. Carpet and heavy curtains also have a high coefficient of absorption as they are made from materials that can trap and absorb sound.

Wood, on the other hand, is a harder material that reflects sound rather than absorbing it, making it less effective for soundproofing purposes.

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