An elevator is descending with uniform acceleration. To determine the acceleration, a person in the elevator drops a coin at the instant the elevator starts. The coin is 6 ft above the elevator floor at the time it is dropped. The person observes that the coin strikes the floor in 1 second. From these data, calculate the acceleration of the elevator in ft/s ^2 .

Step-by-step solution

Let the downward acceleration of the elevator be a . The acceleration of the freely falling coin is g = 32 ft/s ^2 downwards. The relative acceleration of the coin with respect to the elevator is a_ rel = g - a downwards. Since the coin is dropped at the instant the elevator starts, the initial relative velocity of the coin is u_ rel = 0 . The relative displacement of the coin is s_ rel = 6 ft and the time taken is t = 1 s . Using the equation of kinematics for relative motion: s_ rel = u_ rel t + 1 2 a_ rel t^2 Su