the distance d that an object falls varies directly with the

the distance d that an object falls varies directly with the square of the time t of the fall. If an object falls 100 ft in 2 seconds, how long will it take the object to fall 81 ft

Solution

Let the relationship between the distance d that an object falls and the time t be d = kt² where k is an arbitrary constant. Further, when t = 2, d = 100. Therefore, 100 = k*2² or, 4k = 100. Therefore, k = 100/4 = 25. Then, we have d = 25t². Now, when d = 81, we have 81 = 25t², so that t² = 81/25 and t = 81/25 = 9/5 = 1.8 seconds. The answer is 1.8 seconds.