Question

The distance a body falls from rest varies directly as the square of the time it falls (ignoring air resistance). If a ball falls 144 feet in three seconds,

how far will the ball fall in seven seconds ?

A)716 feet
B)767 feet
C) 777 feet
D) 784 feet

Answer 1

Using the direct variation formula for the distance (d) fallen from rest, d = k * t^2, we find that the ball will fall 784 feet in 7 seconds.

Step-by-step explanation:

The distance a body falls from rest varies directly as the square of the time it falls, ignoring air resistance. To solve the problem, we use the direct variation formula, distance d = k * t2, where k is the constant of variation and t is the time in seconds. As given, when t = 3 seconds, d = 144 feet. Therefore, we can find k by 144 = k * 32, which gives us k = 144/9 = 16. Now, we want to find the distance fallen in 7 seconds. We substitute 7 for t in the equation d = 16 * t2 which gives us d = 16 * 72 = 16 * 49 = 784. Therefore, the ball will fall 784 feet in 7 seconds.