1. 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 ft2 of wetted surface area goes in order to experience a drag force of 94N?
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 ft2 of wetted surface area goes in order to experience a drag force of 94N?
Answers & Comments
Answer:
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
Explanation:
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