1. Tardigrade
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  4. A very broad elevator is going up Vertically with a constant acceleration of 2 m/s2. At the instant when its velocity is 4 m/s a ball is projected from the floor of the lift with a speed of 4 m/s relative to the floor at an elevation of 30°. Time taken by the ball to return the floor is (g = 10 m/s2)

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Q. A very broad elevator is going up Vertically with a constant acceleration of $2\, m/s^{2}$. At the instant when its velocity is $4\,m/s$ a ball is projected from the floor of the lift with a speed of $4 \,m/s$ relative to the floor at an elevation of $30^{\circ}$. Time taken by the ball to return the floor is $(g = 10\, m/s^{2})$

Motion in a Plane

Solution:

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Components of velocity of ball relative to lift are:
$u_{x} =4\,\,cos \,\,30^{\circ}=2 \sqrt{3} \,m/s$
$u_{y}= 4 \,sin\, 30^{0} =2 \,m/s$
and acceleration of ball relative to lift is $12\, m/s^{2}$ in negative y-direction or vertically downwards. Hence time of flight
$T=\frac{2u_{y}}{ 12}= \frac{u_{y}}{6}=\frac{2}{6}=\frac{1}{3}s$