A person standing on the floor of an elevator drops a coin. The coin reaches the elevator floor in time t₁ when the elevator is stationary, and in time t₂ when it is moving uniformly. It follows that

Step-by-step solution

Let the height from which the coin is dropped be h . When the elevator is stationary, the initial relative velocity of the coin with respect to the elevator is zero. The relative acceleration of the coin is g downwards. Using the equation of motion S_ rel = u_ rel t + 1 2 a_ rel t^2 , we get h = 1 2 g t₁^2 , which gives t₁ = 2h g . When the elevator is moving uniformly, its acceleration is zero. The frame of reference of the elevator is an inertial frame. The initial relative velocity of the coin with respect to th