Answer to Question #133445 in Other Engineering for Isaac musonda

Question

Ball thrown vertically from 12 m level in elevator
shaft with initial velocity of 18 m/s. At same
instant, open-platform elevator passes 5 m level
moving upward at 2 m/s.
Determine (a) when and where ball hits elevator and
(b) relative velocity of ball and elevator at contact.

Answer 1

Let us write equations of motion of the ball and the elevator:

, ,

, (elevator moves with constant speed upwards),

where:

are initial heights of ball and elevator respectively,

are initial velocities of ball and elevator respectively.

a) When the ball and elevator contact, , from where , or, rearranging terms, .

This is a quadratic equation for time, when they contact. Solving the equation, obtain two roots . We discard the negative solution, hence the ball hits the elevator in at .

b) The velocity of the ball at time is (it is negative, because the ball is moving down). Velocity of the elevator remains , and is directed up, so relative velocity is .