Question

A ball of mass 0.25 kg falls from a height of 50 m. Using energy considerations, find the final velocity. Let g = 9.8 m/s2

With Explanation please
a. 2.97m/s
b. 21.0m/s
c. 33.3 m/s
d. 44.1m/s

Answer 1

For some reason, I got 31.3m/s but I guess thats close enough to C.

Step-by-step explanation:

When the ball is at a height of 50m, this ball has max gravitational potential energy of 122.5J from the formula;

Gravitational Potential Energy (Eₚ) = mgh

Eₚ = 0.25 × 9.8 × 50

Eₚ = 122.5J

When the ball is dropped, it loses height and the gravitational potential energy decreases. This energy is also getting converted into kinetic energy as it falls. Thus, the ball gains kinetic energy. When the ball reaches the bottom (haven't landed yet), the ball has max kinetic energy. Hence, we will take this as the final velocity.

To find this velocity, we use this formula;

Eₖ = 1/2 × m × v²

122.5 = 1/2 × 0.25 × v²

122.5 = 0.125 × v²

v² = 122.5/0.125

v = √980

v = 31.3m/s (3sf)

I hope this helps! Please let me know any misconceptions or miscalculations and feel free to ask me any questions!