Question

a boy throws a ball up into the air with a speed of 8.2 m/s. the ball has a mass of 0.3 kg. how much gravitational potential energy will the ball have at the top of its flight? (assume there is no air resistance.)
a. 10.1 j
b. 19.3 j
c. 15.2 j
d. 8.7 j

Explanation:

Step1: Apply energy - conservation

At the bottom, the ball has only kinetic energy. At the top of its flight, its velocity is 0 and it has only gravitational potential energy. By the conservation of mechanical energy (since there is no air - resistance), the gravitational potential energy at the top ($U$) is equal to the initial kinetic energy ($K$) at the bottom.
The formula for kinetic energy is $K=\frac{1}{2}mv^{2}$, where $m$ is the mass and $v$ is the velocity.

Step2: Substitute the given values

Given $m = 0.3\ kg$ and $v=8.2\ m/s$.
$K=\frac{1}{2}\times0.3\times(8.2)^{2}=\frac{1}{2}\times0.3\times67.24 = 10.086\ J\approx10.1\ J$

Since $U = K$, the gravitational potential energy at the top is approximately $10.1\ J$.

Answer:

A. 10.1 J