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# 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

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#### 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,
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 Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(D) | Q: 2 | Page no. 78

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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.
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