An elevator is accelerating vertically upwards at a rate of g 3 . A person inside the elevator drops a ball from a height h above the elevator floor. What is the time taken for the ball to reach the floor?

Step-by-step solution

Let the upward direction be positive and downward be negative. Acceleration of the elevator, a_ e = + g 3 Acceleration of the freely falling ball with respect to the ground, a_ b = -g The relative acceleration of the ball with respect to the elevator is: a_ rel = a_ b - a_ e = -g - (+ g 3 ) = - 4g 3 The magnitude of relative acceleration is 4g 3 downwards. The initial relative velocity of the ball is zero ( u_ rel = 0 ). Using the second equation of motion for relative motion: s_ rel = u_ rel t + 1 2 a_ rel t^2 h =