Question

The distance a body falls varies directly as the square of the time that it falls. If it falls 972 meters in 18 seconds, how far will it fall in 2 seconds?

Answer 1

Let's use the formula for direct variation to solve this problem. If a quantity varies directly as the square of another quantity, we can write:

distance = k * time^2

where k is a constant of proportionality. To solve for k, we can use the information given in the problem:

972 = k * 18^2

Simplifying this expression, we get:

k = 972 / 324 = 3

Now we can use this value of k to find the distance that the body falls in 2 seconds:

distance = 3 * 2^2 = 12 meters

Therefore, the body will fall 12 meters in 2 seconds.