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Motion in a Straight Line

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Question : 24 of 27
Marks: +1, -0
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^{-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^{-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,u=49\ \mathrm{m}\ \mathrm{s}^{-1},\ a=-9.8\ \mathrm{m}\ \mathrm{s}^{-2},
t=?, x−x0=S=0t=?,\ x-x_{0}=S=0
As, S=ut+12at2S=u t+\frac{1}{2}a t^{2}
∴  0=49t+12(−9.8)t2\therefore\; 0=49 t+\frac{1}{2}(-9.8) t^{2}
or 49t=4.9t249 t=4.9 t^{2}
or t=494.9=10t=\frac{49}{4.9}=10 seconds
As the lift starts moving upwards with uniform speed of 5 m s−1^{-1}, there isno change in the relative velocity of the ball with respect to the boy i.e., itremains 49 m s−1^{-1}. Hence, even in this case, the ball will return to the boy’shand after 10 second.
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