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Question

A ball is thrown vertically upward with a velocity of 10 m/s from the top of a tower of height of 50 m. Find the time taken by the ball to reach a height 10 m from the ground. (Take g=10 m/s2)

A
1 s
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B
3 s
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C
4 s
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D
5 s
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Solution

The correct option is C 4 s
Taking origin O at ground and vertically upward direction as +y axis direction.

Initial velocity of ball:
uy=10 m/s, ux=0
Acceleration of ball:
ay=g=10 m/s2, ax=0
With respect to origin O, the displacement of ball in y-direction when it is at a height 10 m from ground is:
Sy=S2S1=40 m
Using kinematic equation in y-direction:
Sy=uyt+12ayt2
40=10t+12(10)t2
5t210t40=0
t22t8=0
(t4)(t+2)=0
t=4,2
Neglecting -ve value of time, we get:
t=4 s

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