From the top of a 45‑m high roof, a stone is thrown horizontally with speed 25 m/s. Assuming (g=10\text{ m/s}^2) and neglecting air resistance, find (i) the time taken to hit the ground and (ii) the horizontal distance travelled.

Step-by-step solution

1. Step 1: Treat vertical and horizontal motions separately; vertical motion is uniformly accelerated.
2. Step 2: Use (s=\frac12 gt^2) for vertical displacement (s=45\text{ m}).
3. Step 3: Solve for (t): (\frac12cdot10cdot t^2=45\Rightarrow t^2=9\Rightarrow t=3\text{ s}).
4. Step 4: Since horizontal motion is uniform, horizontal distance (x=v_xt).
5. Step 5: Compute (x=25\text{ m/s}\times3\text{ s}=75\text{ m}).
6. Step 6: Conclude time to hit ground is 3 s and horizontal range is 75 m.

Concept tested: horizontal projectile motion

Published 16 October 2026 · How this solution was prepared and checked