A ball is thrown vertically upwards from the level with an initial velocity of . At the same instant an open platform elevator passes the level, moving upwards with a constant velocity of . Determine

1) The ball will meet the elevator in ____ m

2) The relative velocity of the ball with respect to the elevator when the ball hits the elevator ____ m/s.

Question

A ball is thrown vertically upwards from the level with an initial velocity of . At the same instant an open platform elevator passes the level, moving upwards with a constant velocity of . Determine

1) The ball will meet the elevator in m

2) The relative velocity of the ball with respect to the elevator when the ball hits the elevator m/s.

Accepted Answer

Concept- In this question consider the Initial velocity of ball

, initial level of the ball from the ground

, velocity of elevator

(constant velocity, initial level of elevator from the ground

. Then
use a second equation of motion to get the distance travelled by the ball and the elevator. The distance travelled by the elevator must be equal to the distance travelled by the ball to get the first part. For the second part use the concept that the relative velocity of the ball is the difference between the final velocity of the ball and the velocity of the elevator.
Formula used

(A)Initial velocity of ball

Initial position of ball

Acceleration

Substituting these values in the equation for uniformly accelerated motion we get

Now,
Initial velocity of elevator

When ball hit the elevator then

Putting in (1)

(B)Relative velocity of ball wrt the elevator

When the ball hits the elevator at time

we have

The negative sign means that the ball is observed from the elevator to the moving in the negative sense(downward).
Hence, the answer is 1)12.30m
2)-19.81m/s

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