Question

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).

Answer 1

a)the kinetic energy
`E_k=1/2mv^2=0.5*0.5*15^2=56.25J`
b)The gravitatinal potential energy
`E_g=mgh=0.5*9.81*20=98.1 J`
c)`v=19.8m/s`
d)`H_max=31.47m`
`v_max=24.85m/s`

Explanation:

We choose origin of O on the ground
The formula of kinetic energy `E_k=1/2mv^2`
The formula of gravitational potential energy
`E_g=m.g.h`
To solve (d) we apply law of conservation of mechanical energy