A ball is dropped from the top of a building 20 m high. How much time will it take to reach the ground, and with what velocity will it strike the ground ? (Take \(g = 10\ \mathrm{m/s^2}\); neglect air resistance.)

Answer: Time = 2 s; velocity on striking the ground = 20 m/s.

Given: initial velocity u = 0 (dropped), distance s = 20 m, a = g = 10 m/s². This is free fall.

Using Newton’s second equation of motion, \(s = ut + \tfrac12 g t^2\):

\[20 = 0 + \tfrac12 \times 10 \times t^2 \;\Rightarrow\; t^2 = 4 \;\Rightarrow\; t = 2\ \text{s}\]

Using the first equation, \(v = u + gt\):

\[v = 0 + 10 \times 2 = 20\ \text{m/s}\]

Check with the third equation: \(v^2 = u^2 + 2gs = 0 + 2 \times 10 \times 20 = 400\), so v = 20 m/s.