Problema Solution
The drag force F on a boat varies jointly with the wet surface area A of the boat and the square of the speed s of the boat. A boat with a wet surface area of 72 ft^2 traveling at 12.5 mph experiences a drag force of 675 N. Find the wet surface area of a boat traveling 16 mph and experiencing a drag force of 384 N.
Answer provided by our tutors
F varies jointly with A and the square of s means
F = k*A*s^2,
where k is a constant.
First we need to find k using:
A = 72 ft^2
s = 12.5 mph
F = 675 N
675 = k*72*12.5
by solving for k we find
k = 3/4
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the equation for F is
F = (3/4)A*s^2
For s = 16 mph and F = 384 N we need to find A
(3/4)A*16^2 = 384
by solving we find
A = 2 ft^2
click here to see the step by step solution of the equation
the wet surface area is 2 ft^2.