Question

A stone is dropped vertically downwards from the top of a tower of height 45m with a speed of 20m/s. find the;

(a) time it takes to reach the ground.
(b) speed with which it hits the ground.
( take g=10m/s)​

Answer 1

(a) 1.6 s

(b) 36 m/s

Explanation:

Take down to be positive.

Given:

Δy = 45 m

v₀ = 20 m/s

a = 10 m/s²

(a) Find t.

Δy = v₀ t + ½ at²

45 m = (20 m/s) t + ½ (10 m/s²) t²

45 = 20t + 5t²

9 = 4t + t²

13 = t² + 4t + 4

13 = (t + 2)²

t = -2 ± √13

t ≈ 1.6 s

(b) Find v.

v² = v₀² + 2aΔy

v² = (20 m/s)² + 2 (10 m/s²) (45 m)

v = 10√13

v ≈ 36 m/s