Motion in a Straight Line

Question : 24

Total: 27

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:

Taking vertical upward direction as the positive direction of x-axis.When lift is stationary, consider the motion of the ball going verticallyupwards and coming down to the hands of the boy, we have
u=49 m s−1,a=−9.8 m s−2,
t=?,x−x0=S=0
As, S=ut+

at2
∴‌0=49t+

(−9.8)t2
or 49t=4.9t2
or t=

4.9

=10 seconds
As the lift starts moving upwards with uniform speed of 5 m s‌–1, there isno change in the relative velocity of the ball with respect to the boy i.e., itremains 49 m s‌–1. Hence, even in this case, the ball will return to the boy’shand after 10 second.

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