A ball is thrown vertically upward with a velocity of 10m/s from the top of a tower of height of 50m. Find the time taken by the ball to reach a height 10m from the ground. (Take g=10m/s2)
A
1s
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B
3s
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C
4s
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D
5s
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Solution
The correct option is C4s Taking origin O at ground and vertically upward direction as +y axis direction.
Initial velocity of ball: uy=10m/s,ux=0
Acceleration of ball: ay=−g=−10m/s2, ax=0
With respect to origin O, the displacement of ball in y-direction when it is at a height 10m from ground is: Sy=S2−S1=−40m
Using kinematic equation in y-direction: Sy=uyt+12ayt2 ⇒−40=10t+12(−10)t2 ⇒5t2−10t−40=0 t2−2t−8=0 ∴(t−4)(t+2)=0 ⇒t=4,−2
Neglecting -ve value of time, we get: t=4s