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…

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.)\na. 10.1 j\nb. 19.3 j\nc. 15.2 j\nd. 8.7 j

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.)\na. 10.1 j\nb. 19.3 j\nc. 15.2 j\nd. 8.7 j

Answer

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