Theory question 108
DynamicsA stone is dropped vertically downwards from the top of a tower of height 45m with a speed of 20 ms−1. Find the: (a) time it takes to reach the ground; (b) speed with which it hits the ground. [Take g = 10 ms−2]
Show the model answer
Model answer
(a) s = ut + ½gt²: 45 = 20t + 5t², so t² + 4t − 9 = 0.
t = −2 + √13 ≈ 1.61 s.
(b) v² = u² + 2gs = 400 + 900 = 1300, v ≈ 36.06 ms⁻¹.
Explanation
Take downwards as positive; u = 20 and g = 10 both act downwards.