A passenger sitting in a train compartment drops a small bolt from a height h above the floor. Let t₁ be the time taken by the bolt to reach the floor when the train is moving straight along a horizontal track with a constant speed v . Let t₂ be the time taken when the train is completely stationary. Which of the following relationships is correct?

Step-by-step solution

Since the train is moving with a constant speed v along a straight horizontal track, its acceleration is zero. The vertical motion of the bolt is independent of the horizontal uniform motion of the train. The initial vertical velocity of the bolt relative to the train is zero, and the relative vertical acceleration is g downwards. Using the second equation of motion for the relative vertical motion, h = u_ rel t + 1 2 a_ rel t^2 . Since u_ rel = 0 and a_ rel = g , the time taken is t = 2h g . This time is independe