A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.4 ft/s. (a) how rapidly is the area enclosed by the ripple increasing when the radius is 4 feet? the area is increasing at ft2/sft2/s. (b) how rapidly is the area enclosed by the ripple increasing at the end of 9 seconds? the area is increasing at ft2/sft2/s.

Question

Physics

Araceli Meadows

6 May, 02:04

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.4 ft/s. (a) how rapidly is the area enclosed by the ripple increasing when the radius is 4 feet? the area is increasing at ft2/sft2/s. (b) how rapidly is the area enclosed by the ripple increasing at the end of 9 seconds? the area is increasing at ft2/sft2/s.

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Answers (2)

Know the Answer?

Anabel Wallace · Answer 1

Yes they are correct

Scarlett Downs · Answer 2

For the first question which asking how rapid is the area enclosed by the ripple increasing when the radius is 2 feet, we will use the formula which is Area A = pi*r^2 then apply differentiation dA/dt = pi * 2r * dr/dt

A) area enclosed increasing at speed dA/dt = pi * 2 * 2 feet * 2.4 feet/sec

For the second question B) After 9.5 seconds, radius = 9.5 * 2.4 = 22.8 feet area increasing at speed dA/dt = pi * 2 * 22.8feet * 2.4 feet/sec answer units = 343.82 feet^2 / sec