A boy throws up a ball in a stationary lift and the ball returns to his hands in . Now if the lift starts moving up at a speed of . The time taken for a ball thrown straight up to return to his hands is
Step 1: Given data:
The velocity of the lift is
After throwing the ball it returns in when the lift is stationary
The displacement of the ball is zero because the ball will return to its initial point.
Diagram:
Step 2: Formula used
We know from the formulae of kinematics that, the displacement of a body is given by the equation,
Where, and are the displacement and initial velocity of the body, is the acceleration of the body and is the time.
Step 3: Calculation:
Let be the velocity projection of the ball.
The displacement of the body is zero (due to uniform velocity),
Time taken,
So, the velocity of projection of the ball is
When the lift is in motion
Due to uniform motion, the displacement of the lift is,
And the displacement of the ball when the lift is moving up,
Due to uniform motion (velocity of the lift).
The displacement of the ball = displacement of the body. So on equating equations and we get,
Therefore, after, the ball will return.