The​ distance, d, that an object falls is directly proportional to the square of the​ time, t, it has been in free fall. An object that has been in free fall for 3 seconds has fallen 144 feet. Determine the distance the object has fallen if it has been falling for 4 seconds.

Question

d = ? ft

Answer 1

We can set up a proportion to solve this problem.

Since the distance, d, is directly proportional to the square of the time, t, we can write the proportion as:

d₁/t₁² = d₂/t₂²

where d₁ is the distance the object has fallen in t₁ seconds, and d₂ is the distance we want to find in t₂ seconds.

We are given that the object has fallen 144 feet in 3 seconds, so we have:

144/3² = d₂/4²

Simplifying, we get:

144/9 = d₂/16

Cross multiplying, we have:

9 * d₂ = 144 * 16

Solving for d₂, we get:

9 * d₂ = 2304

d₂ = 2304/9 ≈ 256

Therefore, if the object has been falling for 4 seconds, it would have fallen approximately 256 feet.