Question

On a certain planet, a stone weighing 2 kg is thrown vertically downwards with a velocity of 5 m/s from a height of 30 m. It took 4 s to reach the ground. Calculate the work done by gravity.

A. −75 J
B. 60 J
C. −60 J
D. 75 J

Answer 1

The work done by gravity, given that the stone is thrown vertically downwards with a velocity of 5 m/s from a height of 30 m is 75 J (option D)

How to calculate the work done by gravity?

First, we shall calculate the final velocity of the ball on reaching the ground. Details below:

• Initial velocity (u) = 5 m/s
• Height (h) = 30 m
• Time (t) = 4 s
• Final velocity (v) =?

`s = ((v+u)t)/(2) \\\\30 = ((v\ +\ 5)4)/(2) \\\\30 = (v\ +\ 5)2\\\\15 = v\ +\ 5\\\\v = 15 - 5\\\\v = 10\ m/s`

Next, we shall calculate the acceleration due to gravity of the planet. Details below:

• Initial velocity (u) = 5 m/s
• Height (h) = 30 m
• Final velocity (v) = 10 /s
• Acceleration due to gravity of planet (g) =?

`g = (v^2\ -\ u^2)/(2h) \\\\g = (10^2\ -\ 5^2)/(2\ *\ 30)\\\\g = 1.25\ m/s^2`

Finally, we shall calculate the work done by gravity. This is shown below:

• Mass of stone (m) = 2 Kg
• Acceleration due to gravity of planet (g) = 1.25 m/s²
• Height (h) = 30 m
• Work done by gravity =?

Work done by gravity = mgh

= 2 × 1.25 × 30

= 75 J

The answer is option D