The air resistance R(in pounds) on a racing cyclist is given by the equation R=0.00829s^2 where s is the bicycle's speed (in miles per hour).

a. What is the speed of a racing cyclist who experiences 5 pounds of air resistance?

b. What happens to the air resistance if the cyclist's speed doubles? How would I justify the answer for b algebraically?

1 answer

.00829s^2 = 5
s^2 = 560.538
s = 23.67

R(2s) = .00829(2s)^2 = .00829*4s^2 = 4R(s)

That is, if s is multiplied by a factor k, R increases by a factor of k^2