__Question 3.24__

__A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 m s__

^{-1}. How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of 5 m s

^{-1}and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands ?

__Solution:__

Initial velocity of the ball,

*u*= 49 m/s

Acceleration,

*a*= – g = – 9.8 m/s

^{2}

^{}

*Case*I:

When the lift was stationary, the boy throws the ball.

Taking upward motion of the ball,

Final velocity,

*v*of the ball becomes zero at the highest point.

From first equation of motion, time of ascent (

*t*) is given as:

v = u +at

t = (v - u)

**/**a

= -49

**/**-9.8 = 5 s

But, the time of ascent is equal to the time of descent.

Hence, the total time taken by the ball to return to the boy’s hand = 5 + 5 = 10 s.

*Case*II:

The lift was moving up with a uniform velocity of 5 m/s. In this case, the relative velocity of the ball with respect to the boy remains the same i.e., 49 m/s. Therefore, in this case also, the ball will return back to the boy’s hand after 10 s.

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