Help with joint variation problem

Question

The drag force on a boat varies jointly as the wetted surface area and the square of the velocity of a boat. If a boat going 6.5 mph experiences a drag force of 86 N when the wetted surface area is 41.2 ft2, how fast must a boat with 28.5 ft2of wetted surface area go in order to experience a drag force of 94N?

Answer 1

We are given the following relationship:

F = k * a * v * v

where k is a constant characteristic of a particular boat, a is the wetted surface area, and v is the velocity of the boat.

For the first data set we have:

86N = k * 41.2ft2 * 6.5mph * 6.5mph

or

k = 0.0494

For the second data set the only unknown is the velocity, so:

v = sqrt( F / k / a ) = sqrt ( 94N / 0.0494 / 28.5ft2 ) = 8.171mph