An object is thrown vertically upwards from the top of a cliff with a velocity of \(25ms^{-1}\). Find the time, in seconds, when it is 20 metres above the cliff. \([g = 10ms^{-2}]\).
A. 0 and 1 B. 0 and 4 C. 0 and 5 D. 1 and 4
Correct Answer: D
Explanation
\(s = ut + \frac{at^{2}}{2}\) This movement is against gravity, so it is negative. \(s = ut - \frac{gt^{2}}{2}\) \(s = 20m, u = 25ms^{-1}\) \(20 = 25t - \frac{10t^{2}}{2} \implies 20 = 25t - 5t^{2}\) \(5t^{2} - 25t + 20 = 0 \) \(5t^{2} - 5t - 20t + 20 = 0 \implies 5t(t - 1) - 20(t - 1) = 0\) \(5t - 20 = \text{0 or t - 1 = 0}\) \(t = \text{1 or 4}\)
