Calculus, 8th Edition,stewart; page 44 problem 55

Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.

(a) Express the radius r of this circle as a function of the time t (in seconds).

(b) If A is the area of this circle as a function of the radius, find A o r and interpret it.

Answer 1

Step:1

Circular ripple travels outward with a speed of  cm/sec.

(a)

Consider time taken by the circular ripple to travel a distance  is  sec.

Speed-distance relation :

The distance traveled by the circular ripple is

.

Step:2

(b)

Find .

Area of circle is .

                                               ( Since  )

                

Area of circular ripple is  sqcm.

Solution:

(a) The distance traveled by the circular ripple is .

(b) Area of circular ripple as the function of time  is  sqcm.