Question

The vertical distance of a falling ball is directly proportional min to the square of the time of the fall. The ball falls 80 m 4 seconds.

(a) Find the vertical distance fallen in 6 seconds.

(b) If the ball is dropped from a height of 240 m, find the time it takes to hit the ground.

Answer 1

180 m , ≈ 6.9 seconds

Explanation:

let vertical distance be represented by d and time t

given d is directly proportional to t² , then the equation relating them is

d = kt² ← k is the constant of proportion

to find k use the condition , the ball falls 80 m in 4 seconds , then

80 = k × 4² = 16k ( divide both sides by 16 )

5 = k

d = 5t² ← equation of proportion

(a)

when t = 6

d = 5 × 6² = 5 × 36 = 180 m

(b)

when d = 240

240 = 5t² ( divide both sides by 5 )

48 = t² ( take square root of both sides )

`√(48)` = t , that is

t ≈ 6.9 seconds ( to the nearest tenth )