Instantaneous Rate Word Problems

[leibnitz2001]

1. Water is draining out of a conical tank at a constant rate of 4 feet cubed per minute. Before the tank began draining, the depth of water was 12 ft and the diameter of the waters surface was 8 ft. How fast will the water level be falling when half the water has drained from the tank?

2. A submarine passes directly beneath an enemy destroyer. The sub is 200 ft below the surface of the water, moving northeastward at 40 mi per hour. The destroyer is sailing due south at 25 mi per hr. At what rate will the vessels be seperating after 1/2 hour?

I have figured out a solution for the first problem, but for some reason, even after several attempts, the answer did not match that in the book.

The second problem has given me a little more problem in that I cannot find a proper set up for the problem.

Note that also, these problems are to be done without use of the chain rule or trigonometric differentiation: all that is at your disposal are the basic product, sum, difference, quotient rules of differentiation.

For differentiating a cube root function, this equation comes in handy, which is derived from the product rule:

If f(x)=cube root of g(x), then f'(x) equals g'(x)/(3 times cube root of g(x)^2)

I am interesting in some other solutions to these problems you might be able to provide.

Thanks

 

[NSX]

Have you tried drawing a picture?

 

[leibnitz2001]

As I said, I have found solutions to both of the problems. The issue is that my answer is not matching that with the book, despite the fact that I have redone the problems numerous times.