Question

A 3 kg ball is dropped from a height of 100 m above the surface of Planet Z. If the ball reaches a velocity of 45 m/s in 7 s, what is the ball’s weight on Planet Z? What is the gravitational field strength on Planet Z?

Answer 1

We are given the following information

Mass of ball = 3 kg

Height = 100 m

Final velocity = 45 m/s

Time = 7 s

Recall from the equations of motion

`s=u\cdot t+(1)/(2)\cdot g\cdot t^2`

Where u is the initial velocity of the ball that is zero.

`\begin{gathered} s=u\cdot t+(1)/(2)\cdot g\cdot t^2 \\ 100=0\cdot7+(1)/(2)\cdot g\cdot7^2 \\ 100=(1)/(2)\cdot g\cdot49 \\ g=(2\cdot100)/(49) \\ g=4.08\; (m)/(s^2) \end{gathered}`

So, the gravitational acceleration of the planet Z is 4.08 m/s^2

The weight o the ball is given by

`\begin{gathered} W=m\cdot g \\ W=3\cdot4.08 \\ W=12.24\; N \end{gathered}`

Therefore, the weight of the ball is 12.24 N