Question

The radius of a hailstone varies directly with

the amount of time that it was in a cloud.

After a hailstone had been in a particular

cloud for 10 seconds, its radius was 0.5

inches. How long would it have to be in the

cloud to have a radius of 1.25 inches?

Answer 1

Hailstone remained in the cloud for 25 seconds.

Explanation:

Radius of a hailstone varies directly with the duration for which it was in the cloud.

Let the radius of the hailstone is 'r' and it was in the cloud for 't' seconds.

r ∝ t

r = kt [ k is the proportionality constant]

If r = 0.5 inches and t = 10 seconds

Then, 0.5 = k × 10

k =
`(0.5)/(10)`

k = 0.05

Now we have to find the duration t for which hailstone was in the cloud having radius = 1.25 inches.

1.25 = 0.05 × t

t =
`(1.25)/(0.05)`

t = 25 second

Therefore, hailstone remained in the cloud for 25 seconds.