Question

A stone is thrown vertically downwards and the formula d = 16t² + 4t gives the distance, d metres, that it falls in t seconds. How long does it take to fall 420 metres?

Answer 1

From the given information,

16t² + 4t = 420

4t² + t – 105 = 0

4t² – 20t + 21t – 105 = 0

4t(t – 5) + 21(t – 5) = 0

(4t + 21)(t – 5) = 0

`t = -21/4, 5`

But, time cannot be negative.

Thus, the required time taken is 5 seconds.