We have the right to use potential energy to solve. Remember, her height and your gravity need to have actually the exact same sign, together they are relocating in the exact same direction (downward). Either do them both negative, or usage an absolute value.

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Using conservation of energy, we recognize that

. This tells united state that the potential power at the optimal of the hill is every converted to kinetic energy at the bottom that the hill. We have the right to substitute the equations because that potential energy and kinetic energy.The masses publication out.

Plug in the values, and also solve for the velocity.

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### Example question #2 : Calculating Kinetic power

A

ball rolls under a hill through an early velocity that . What is its best velocity?**Possible Answers:**

**Correct answer:**

Explanation:

For this problem, the ball starts with both potential and also kinetic energy. The point of best velocity will have actually no potential energy. We can solve setup the early energy and also final power equal, due to conservation of energy.

The masses will cancel out from all of the terms.

Plug in the offered values and solve for the last velocity. Remember, once the round is top top the floor it has a elevation of zero.

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### Example concern #3 : Calculating Kinetic power

A book falls off of a

high table. If the book weighs , what will certainly its final velocity be right before it access time the ground?**Possible Answers:**

**Correct answer:**

Explanation:

The publication initially has actually only potential energy. Right prior to it hits the ground, every the potential power will be convert to kinetic energy. We can use the legislation of conservation of energy to collection the initial and final energies equal.

Use the equations because that potential energy and also kinetic energy.

Now, plugin the values given to you in the problem and also solve because that the velocity.

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### Example inquiry #4 : Calculating Kinetic energy

A book falls turn off of a

high table. If the publication weighs , what will its kinetic power be right before it access time the ground?**Possible Answers:**

**Correct answer:**

Explanation:

Initially, the publication has just potential energy. Right prior to it access time the ground, all the potential power will have actually converted come kinetic energy. The 2 values will be equal based upon the conservation of energy.

If we fix for potential, us can discover kinetic energy.

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### Example question #5 : Calculating Kinetic energy

A rock is dropped indigenous a helicopter hovering at

above the ground. If the absent weighs , what is that is kinetic energy right before it access time the ground?**Possible Answers:**

**Correct answer:**

Explanation:

Right before it access time the ground, the initial potential energy and also the last kinetic power will equal each other as result of conservation the energy.

If we resolve for early stage potential, us can find final kinetic energy.

Plug in the worths given. Mental that elevation is the change in height. Since the absent is top downward, the elevation will be negative.

Multiply and also solve.

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### Example question #6 : Calculating Kinetic power

A pendulum through string length

is dropped indigenous rest. If the mass at the end of the pendulum is , what is its preferably velocity?**Possible Answers:**

**Correct answer:**

Explanation:

The best velocity that the pendulum will be once the object has actually only kinetic energy. Using conservation that energy, we can set our early stage potential energy to equal our "final" kinetic energy.

Plug in the provided values and solve for the velocity.

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### Example inquiry #7 : Calculating Kinetic power

A

book falls off the height of a bookshelf. What is its final velocity right prior to it access time the ground?**Possible Answers:**

**Correct answer:**

Explanation:

The relationship between velocity and also energy is:

We understand the mass, yet we require to find the complete kinetic energy.

Remember the legislation of preservation of energy: the complete energy at the start equals the full energy at the end. In this case, we have only potential power at the beginning and only kinetic power at the end. (The early stage velocity is zero, and the final height is zero).

If we can find the potential energy, we can uncover the kinetic energy. The formula because that potential energy is

.Using our provided values for the mass, height, and gravity, we deserve to solve using multiplication. Note that the height becomes an unfavorable because the book is travel in the bottom direction.

The kinetic power will additionally equal

, as result of conservation the energy.Using this value and our offered mass, we deserve to calculate the velocity from our initial kinetic energy equation.

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Since we space taking the square root, our answer have the right to be either an unfavorable or positive. The final velocity of the book will it is in in the downward direction; thus, our final velocity should be negative.