### All AP Physics 1 Resources

## Example Questions

### Example Question #133 : Linear Motion And Momentum

An arrow is shot from a height of with an initial velocity of at an angle of above the horizontal. What is the horizontal distance traveled by the arrow before hitting the ground? Neglect air resistance.

**Possible Answers:**

**Correct answer:**

We can use the range equation to calculate how far the arrow travels until it gets back its initial height. However, we then need to calculate how far the arrow travels from there until it hits the ground. So, beginning with the range equation:

Plugging in our values:

Now we need to calculate the horizontal distance that the arrow travels after this point. First, let's calculate how long it takes to hit the ground. At this point, the arrow has the same speed that it began with, but its velocity is now directed at below the horizontal. Therefore, its vertical component:

Then using the following kinematic equation:

Plugging in our values:

Rearranging:

Then using the quadratic formula, we get:

or

Obviously, we can't have a negative time, so the first option is the correct one. We can then multiply this by the horizontal component of the arrow's velocity, which is constant since we are neglecting air resistance, to get the rest of the horizontal distance traveled:

Then adding our two distances together to get our total distance traveled, we get:

### Example Question #404 : Ap Physics 1

An arrow of mass is shot at an angle of above the horizontal with an initial velocity of from a height of and hits a target that is also at a height of and an unknown distance from where the arrow was shot from. If the target absorbs all of the energy from the arrow, how much energy does it absorb? Neglect air resistance.

**Possible Answers:**

**Correct answer:**

The key component of the problem statement is that the arrow is shot from a height of 1m and hits a target that is also at 1m. Therefore, since we are neglecting air resistance, we can conclude that the arrow hits the target at the same speed that it begins with, except that the velocity is now oriented below the horizontal. Thus, the arrow hits the target with the same kinetic energy that it begins with, and the target absorbs all of this energy. Therefore, we can say:

Note that with the information given in the problem statement, the angle that the arrow was shot from and the distance the target was from where the arrow was shot are both insignificant.

### Example Question #41 : Motion In Two Dimensions

An archer has a bow, which can be modeled as a spring. The bow has a spring constant of (that is, for each meter that the string of the bow is pulled back from equilibrium, 700N of force is applied). If the archer pulls back the bow with an arrow of mass and releases it at an angle of above the horizontal, what is the range of the arrow? Neglect air resistance.

**Possible Answers:**

**Correct answer:**

Since the problem statement tells us that the bow can be modeled as a spring, we can use the following expression to determined how much energy is stored in the bow:

Where is the spring constant, and is the distance the string of the bow is pulled from equillibrium. Plugging in our values, we get:

Then we can assume that all of this energy is transferred to the arrow as kinetic energy:

Rearranging for initial velocity:

Plugging in our values:

Then we can use the range equation to calculate the range of the arrow. Since we were given no initial or final heights in the problem statement, we will assume that the initial and final heights are the same; thus, the range equation is applicable:

### Example Question #42 : Motion In Two Dimensions

An arrow is shot from a height of and at an angle of above the horizontal. If the arrow reaches a maximum height of , what was the arrows initial velocity? Neglect air resistance.

**Possible Answers:**

**Correct answer:**

We can use the following kinematic equation to determine the arrow's initial vertical velocity:

Rearranging for initial velocity, and eliminating final velocity:

Substituting in values:

Then using the following equation to determine total initial velocity:

Rearranging for initial velocity:

Plugging in our values:

### Example Question #43 : Motion In Two Dimensions

If an arrow is shot with a horizontal velocity of from a height of and travels before hitting the ground, at what angle to the horizontal was the arrow shot at? Neglect air resistance.

**Possible Answers:**

**Correct answer:**

We can use the range equation to solve this problem:

Now let's start to rearrange for theta:

Let's stop here and develop an expression for initial velocity in terms that we know"

Rearranging:

Now let's plug this back into the range equation:

Then we can use the following trig identity:

Plugging this into our expression:

Now we can cancel out a cos function to get:

And then:

Rearranging for theta:

We have values for each of these variables, so time to plug and chug:

### Example Question #44 : Motion In Two Dimensions

An object with mass slides down an incline plane with slope and height . What does the coefficent of friction have to be in order for the object to not gain velocity?

**Possible Answers:**

**Correct answer:**

In order for the object not to gain velocity, all the forces acting on it need to cancel out. The normal force will already cancel with the perpendicular force due to gravity () by definition. In order to find the correct coefficient of friction, we set the magnitude of the force due to friction equal to that of the parallel force due to gravity :

The mass and gravity cancel here.

### Example Question #41 : Motion In Two Dimensions

A ball near the surface of the earth has initial velocity . Determine the velocity seconds later.

**Possible Answers:**

None of these

**Correct answer:**

Using

### Example Question #46 : Motion In Two Dimensions

A car traveling at launches off a ramp of height and length . Determine the maximum height of the car. Ignore air resistance.

**Possible Answers:**

None of these

**Correct answer:**

Finding the angle at which the car launches at:

Determining y-component of velocity:

Using conservation of energy in a closed system:

Initially, the car has both kinetic and gravitational potential energy in the y direction, but after, it only has gravitational potential.

Solving for

Plugging in values:

### Example Question #47 : Motion In Two Dimensions

A car traveling at launches off a ramp of height and length . Determine the "hang time" of the car. Ignore air resistance.

**Possible Answers:**

None of these

**Correct answer:**

Finding the angle at which the car launches at:

Determining component of velocity:

Using conservation of energy in a closed system:

Initially, the car has both kinetic and gravitational potential energy in the y direction, but after, it only has gravitational potential.

Solving for

Plugging in values:

Determine the velocity in the y direction when the car hits the ground

Solving for

Plugging in values:

Now, breaking the jump into two parts, the "up" and the "down" and using

Up:

Down:

### Example Question #48 : Motion In Two Dimensions

A car traveling at launches off a ramp of height and length . Determine the horizontal distance traveled while airborne. Ignore air resistance.

**Possible Answers:**

None of these

**Correct answer:**

Finding the angle at which the car launches at:

Determining component of velocity:

Using conservation of energy in a closed system:

Initially, the car has both kinetic and gravitational potential energy in the y direction, but after, it only has gravitational potential.

Solving for

Plugging in values:

Determine the velocity in the y direction when the car hits the ground

Solving for

Plugging in values:

Now, breaking the jump into two parts, the "up" and the "down" and using

Up:

Down:

Multiplying by the horizontal velocity:

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