#### 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?

#### Solution

From the given information,

16t^{2} + 4t = 420

4t^{2} + t – 105 = 0

4t^{2} – 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.

Is there an error in this question or solution?

Solution 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? Concept: Quadratic Equations.