# High School Physics : Calculating Kinetic Energy

## Example Questions

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### Example Question #1 : Calculating Kinetic Energy

A ball is dropped from  above the ground. Assuming gravity is , what is its final velocity?

Explanation:

We can use potential energy to solve. Remember, your height and your gravity need to have the same sign, as they are moving in the same direction (downward). Either make them both negative, or use an absolute value.

Using conservation of energy, we know that . This tells us that the potential energy at the top of the hill is all converted to kinetic energy at the bottom of the hill. We can substitute the equations for potential energy and kinetic energy.

The masses cancel out.

Plug in the values, and solve for the velocity.

### Example Question #2 : Calculating Kinetic Energy

A  ball rolls down a  hill with an initial velocity of . What is its maximum velocity?

Explanation:

For this problem, the ball starts with both potential and kinetic energy. The point of maximum velocity will have no potential energy. We can solve setting the initial energy and final energy equal, due to conservation of energy.

The masses will cancel out from all of the terms.

Plug in the given values and solve for the final velocity. Remember, when the ball is on the ground it has a height of zero.

### Example Question #2 : Calculating Kinetic Energy

A book falls off of a  high table. If the book weighs , what will its final velocity be right before it hits the ground?

Explanation:

The book initially has only potential energy. Right before it hits the ground, all the potential energy will be converted to kinetic energy. We can use the law of conservation of energy to set the initial and final energies equal.

Use the equations for potential energy and kinetic energy.

Now, plug in the values given to you in the problem and solve for the velocity.

### Example Question #3 : Calculating Kinetic Energy

A book falls off of a  high table. If the book weighs , what will its kinetic energy be right before it hits the ground?

Explanation:

Initially, the book has only potential energy. Right before it hits the ground, all the potential energy will have converted to kinetic energy. The two values will be equal based on the conservation of energy.

If we solve for potential, we can find kinetic energy.

### Example Question #4 : Calculating Kinetic Energy

A rock is dropped from a helicopter hovering at  above the ground. If the rock weighs , what is its kinetic energy right before it hits the ground?

Explanation:

Right before it hits the ground, the initial potential energy and the final kinetic energy will equal each other due to conservation of energy.

If we solve for initial potential, we can find final kinetic energy.

Plug in the values given. Remember that height is the change in height. Since the rock is headed downward, the height will be negative.

Multiply and solve.

### Example Question #4 : Calculating Kinetic Energy

A pendulum with string length  is dropped from rest. If the mass at the end of the pendulum is , what is its maximum velocity?

Explanation:

The maximum velocity of the pendulum will be when the object has only kinetic energy. Using conservation of energy, we can set our initial potential energy to equal our "final" kinetic energy.

Plug in the given values and solve for the velocity.

### Example Question #6 : Calculating Kinetic Energy

book falls off the top of a  bookshelf. What is its final velocity right before it hits the ground?

Explanation:

The relationship between velocity and energy is:

We know the mass, but we need to find the total kinetic energy.

Remember the law of conservation of energy: the total energy at the beginning equals the total energy at the end. In this case, we have only potential energy at the beginning and only kinetic energy at the end. (The initial velocity is zero, and the final height is zero).

If we can find the potential energy, we can find the kinetic energy. The formula for potential energy is .

Using our given values for the mass, height, and gravity, we can solve using multiplication. Note that the height becomes negative because the book is traveling in the downward direction.

The kinetic energy will also equal , due to conservation of energy.

Using this value and our given mass, we can calculate the velocity from our original kinetic energy equation.

Since we are taking the square root, our answer can be either negative or positive. The final velocity of the book will be in the downward direction; thus, our final velocity should be negative.

### Example Question #23 : Energy

book falls off the top of a  bookshelf. What is its velocity right before it hits the ground?

Explanation:

The relationship between velocity and energy is:

We know the mass, but we need to find the total kinetic energy.

Remember the law of conservation of energy: the total energy at the beginning equals the total energy at the end. In this case, we have only potential energy at the beginning and only kinetic energy at the end. (The initial velocity is zero, and the final height is zero).

If we can find the potential energy, we can find the kinetic energy. The formula for potential energy is .

Using our given values for the mass, height, and gravity, we can solve using multiplication. Note that the height becomes negative because the book is traveling in the downward direction.

The kinetic energy will also equal , due to conservation of energy.

Using this value and our given mass, we can calculate the velocity from our original kinetic energy equation.

Since we are taking the square root, our answer can be either negative or positive. The final velocity of the book will be in the downward direction; thus, our final velocity should be negative.

### Example Question #8 : Calculating Kinetic Energy

An orange falls off of a tree  tall. What is the final velocity of the orange before it hits the ground?

Explanation:

For this problem, we need to use the law of conservation of energy. Since we are only looking at gravitational energy here and the orange starts at rest, we can say that the initial potential energy is equal to the final kinetic energy.

.

From here, we can expand the equation, using the formulas for gravitational potential energy and kinetic energy.

Notice that the mass cancels out form both sides.

For the height, make sure to keep that value negative as we are measuring the DISPLACEMENT rather than the distance travelled. Since displacement is a vector (magnitude and direction) we need to be clear that it travels down .

At this point, we need to remember that the square root of a positive number can be either positive or negative. Our velocity is a vector, so we will need to make sure we pick the answer choice with the appropriate direction. Since the orange is traveling downward, we know our final velocity must be negative.

### Example Question #5 : Calculating Kinetic Energy

A baseball has a mass of . If a high school pitcher can throw a baseball at , what is the approximate kinetic energy associated with this pitch?