varies directly

Question

For a body falling freely from rest (disregarding air resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 400 feet high and hits the ground in 5 seconds, how far did it fall in the first 3 seconds?

Answer 1

Notice that D(t) ∝ t² Thus D(t₂) / D(t₁) = (t₂ / t₁)².

 

Thus in 3 seconds it fell D(3) = (3/5)² D(5) = (9/25)(400) = 144 feet.