A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
(a) after 1 s
(b) after 4 s
(c) after 6 s
Answers must be in cm^2/s
The professor did not go over this type of problem in class, and the textbook does not explain it either. I have no idea where to even begin with this problem.
Could someone please explain step by step how to do this? I would really, really appreciate it!
(a) after 1 s
(b) after 4 s
(c) after 6 s
Answers must be in cm^2/s
The professor did not go over this type of problem in class, and the textbook does not explain it either. I have no idea where to even begin with this problem.
Could someone please explain step by step how to do this? I would really, really appreciate it!
-
r = v t
A = π r²
dA/dt = 2π r (dr/dt)
dA/dt = 2π v t * v
dA/dt = 2π v² t
at t = 1s
dA/dt = 2π (40)² (1)
dA/dt = 3200π cm^2/s
A = π r²
dA/dt = 2π r (dr/dt)
dA/dt = 2π v t * v
dA/dt = 2π v² t
at t = 1s
dA/dt = 2π (40)² (1)
dA/dt = 3200π cm^2/s