Question

1. The distance d through which a stone falls from rest is proportional

to the square of the time taken t. If the stone falls 45 m in 3 seconds,
how far will it fall in 6 seconds? How long will it take to fall 20 m?

Answer 1

In 6 seconds: 180 m

20 m: in 2 seconds

Explanation:

y = distance

x = time

y is proportional to x:

y = kx

y is proportional to the square of x:

y = kx²

We are given: (3, 45)

45 = k × 3²

45 = 9k

k = 5

The equation is:

y = 5x²

When x = 6,

y = 5(6²)

y = 180

180 m in 6 seconds

When y = 20,

20 = 5x²

x² = 4

x = 2

2 seconds for 20 m