(a) Calculates the height of a cliff if it takes 2 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.00 m/s. (6) How long would it take to reach the ground if it is thrown straight down with the same speed?
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Explanation:
let h be the height of cliff.
case I) :
initial velocity u = - 8 m/s
time taken t = 2s
displacement s = ut + 1/2 gt²
h = ( -8) x 2 + 1/2 x 10 x 4
= - 16 + 20
= 4 m
Height of cliff = 4 m
case ii) :
u = 8 m/s
s = ut + 1/2 gt²
4 = 8 t + 1/2 x 10 x t²
4 = 8t + 5 t²
5t² + 8t - 4 = 0
5t² + 10t - 2t - 4 = 0
5t (t + 2) - 2 (t + 2) = 0
( t + 2) (5t - 2) = 0
t = - 2 or. t = 2/5
since t > 0
t = 2/5 = 0. 4 s
It reaches the ground in 0.4 s if it is thrown downwards with same speed.
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