# 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? - Mathematics

Sum

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,
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.

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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 6 Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6 (D) | Q 2 | Page 78