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: Option 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})