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Question

A ball thrown vertically upwards with a speed of 20m/s from the top of a tower reaches a certain height and then falls back to the earth in 6 s. Find the height of the tower. [Take acceleration due to gravity, g=10 m/s2]


A

150 m

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B

None of these

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C

160 m

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D

100 m

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Solution

The correct option is C

160 m


Let the height reached by the ball when thrown upwards be H and the height of the tower be h.

Here,

Initial velocity, u=20 m/s

Final velocity after reaching height, H is v=0

acceleration, a=g=10 m/s2 [It is taken as negative because the direction of acceleration due to gravity is downwards, while the initial velocity is upwards]

Using, v2=u2+2as

0=2022gH

H=2022g=20×2020=20 m

Now, the ball will fall down from a height of 20 m from above the tower.

Initial velocity, u=0

time, t=6 s

displacement, s=20+h

acceleration, a=g=10 m/s2

Using s=ut+12at2,

20+h=0×6+12×10×6×6

20+h=180

h=18020=160 m

Thus, the height of the tower is 160 m


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