Question

Flashlight problem: you shine a flashlight, making a circular spot of light on the wall with radius 5cm. As you back away from the wall, the radius increases at the rate of 7 cm/s. Find the radius at times 4s and 7s after you start backing away.

Answer 1

It is given that the radius increases at the rate of 7 cm per second, that is 7 cm in 1s.

It follows that after 4s since backing away, the increase in radius is:

`7*4=28\text{ cm}`

Add the increase to the initial length of the radius:

`28+5=33\text{ cm}`

Hence, the radius 4s after you start backing away is 33 cm.

After 7s, the increase in radius will be:

`7*7=49\text{ cm}`

Add this increase to the initial length of the radius:

`49+5=54\text{ cm}`

Hence, the radius 7s after you start backing away is 54 cm.