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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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