Question

A Cuban athlete Javier Sotomayor set the world record for the high jump. The gravitational potential energy associated with Sotomayor's jumpwas 1,970. J Sotomayor's mass was 82.0 kg. How high did Sotomayor jump?

Answer 1

We are given that an athlete increases his height using an amount of energy equivalent to 1970 Joules. Since the energy associated with the height of an object is the gravitational potential energy this means that the energy and the height are related by the following formula:

`E=mgh`

Where:

`\begin{gathered} E=\text{ energy} \\ m=\text{ mass} \\ g=\text{ acceleration of gravity} \\ h=\text{ height} \end{gathered}`

Now, we solve for the height by dividing both sides by "mg":

`(E)/(mg)=h`

Now, we plug in the values:

`(1970J)/((82kg)(9.8(m)/(s^2)))=h`

Now, we solve the operations:

`2.5m=h`

Therefore, the height was 2.5 meters.