# A 0.5kg rubber ball is thrown straight up into the air. At a height of 20m above the ground, it is travelling at 15m/s. How do you answer the following questions?

## a. What is the ball's kinetic energy at this point? b. What is its gravitational potential energy relative to the ground? c. If all of the ${E}_{g}$ the ball has in part b was originally ${E}_{k}$ at the ground, calculate how fast the ball was travelling initially when it was thrown up in the air. d. Determine the maximum height and velocity reached by the ball (assuming it started at ground level).

May 15, 2016

a)the kinetic energy
${E}_{k} = \frac{1}{2} m {v}^{2} = 0.5 \cdot 0.5 \cdot {15}^{2} = 56.25 J$
b)The gravitatinal potential energy
${E}_{g} = m g h = 0.5 \cdot 9.81 \cdot 20 = 98.1 J$
c)$v = 19.8 \frac{m}{s}$
d)${H}_{\max} = 31.47 m$
${v}_{\max} = 24.85 \frac{m}{s}$

#### Explanation:

We choose origin of O on the ground
The formula of kinetic energy ${E}_{k} = \frac{1}{2} m {v}^{2}$
The formula of gravitational potential energy
${E}_{g} = m . g . h$
To solve (d) we apply law of conservation of mechanical energy