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## Example Questions

### Example Question #1 : Understanding Conservation Of Momentum

A man with a mass of is painting a house. He stands on a tall ladder of height . He leans over and falls straight down off the ladder. If he is in the air for seconds, what will be his momentum right before he hits the ground?

**Possible Answers:**

**Correct answer:**

The problem tells us he falls vertically off the ladder (straight down), so we don't need to worry about motion in the horizontal direction.

The equation for momentum is:

We can assume he falls from rest, which allows us to find the initial momentum.

.

From here, we can use the formula for impulse:

We know his initial momentum is zero, so we can remove this variable from the equation.

The problem tells us that his change in time is seconds, so we can insert this in place of the time.

The only force acting upon man is the force due to gravity, which will always be given by the equation .

### Example Question #2 : Understanding Conservation Of Momentum

A ball is thrown west at and collides with a ball while in the air. If the balls stick together in the crash and fall straight down to the ground, what was the velocity of the second ball?

**Possible Answers:**

**Correct answer:**

We know that if the balls fell straight down after the crash, then the total momentum in the horizontal direction is zero. The only motion is due to gravity, rather than any remaining horizontal momentum. Based on conservation of momentum, the initial and final momentum values must be equal. If the final horizontal momentum is zero, then the initial horizontal momentum must also be zero.

In our situation, the final momentum is going to be zero.

Use the given values for the mass of each ball and initial velocity of the first ball to find the initial velocity of the second.

The negative sign tells us the second ball is traveling in the opposite direction as the first, meaning it must be moving east.

### Example Question #3 : Understanding Conservation Of Momentum

A car travelling at rear ends another car at rest. The two bumpers lock and the cars move forward together. What is their final velocity?

**Possible Answers:**

**Correct answer:**

This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, , we can set up the following equation.

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the velocity of the first car is given. Plug in these values and solve for the final velocity.

### Example Question #4 : Understanding Conservation Of Momentum

A car strikes a car at rest from behind. The bumpers lock and they move forward together. If their new final velocity is equal to , what was the initial speed of the first car?

**Possible Answers:**

**Correct answer:**

This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, , we can set up the following equation.

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the final velocity is given. Plug in these values and solve for the initial velocity of the first car.

### Example Question #2 : Understanding Conservation Of Momentum

A ball moving at strikes a ball at rest. After the collision the ball is moving with a velocity of . What is the velocity of the second ball after the collision?

**Possible Answers:**

**Correct answer:**

We can use the law of conservation of momentum:

We know the mass of each ball and their initial velocities.

We also know the final velocity of the first ball. This leaves only one variable: the final velocity of the second ball.

Solve to isolate the variable.

### Example Question #5 : Understanding Conservation Of Momentum

A ball moving at strikes a second ball at rest. After the collision the ball is moving with a velocity of and the second ball is moving with a velocity of . What is the mass of the second ball?

**Possible Answers:**

**Correct answer:**

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for the mass of the second ball.

### Example Question #6 : Understanding Conservation Of Momentum

A ball strikes a second ball at rest. After the collision the ball is moving with a velocity of and the second ball is moving with a velocity of . What is the initial velocity of the first ball?

**Possible Answers:**

**Correct answer:**

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for the initial velocity of the first ball.

### Example Question #7 : Understanding Conservation Of Momentum

A car with mass and initial velocity strikes a car of mass , which is at rest. If the two cars stick together after the collision, what is the final velocity?

**Possible Answers:**

**Correct answer:**

We know that the cars stick together after the collision, which means that the final velocity will be the same for both of them. Using the formula for conservation of momentum, we can start to set up an equation to solve this problem.

First, we will write the initial momentum.

We know that the second car starts at rest, so this equation can be simplified.

Now we will write out the final momentum. Keep in mind that both cars will have the same velocity!

Set these equations equal to each other and solve to isolate the final velocity.

This is our answer, in terms of the given variables.

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