Question

When a baseball flies through the air, the ratio fquad/flin of the quadratic to the linear drag force is given by
f quad/ f linear = (1.6×10^3 s/m^2) Dv
Given that the baseball has a diameter of 7 cm,
a. Find the approximate speed v at which the linear and quadratic drag forces are equally important?
b. For what speeds is it a good approximation to ignore the linear term and to treat the drag force as purely quadratic?
c. Repeat the previous two questions for a beach ball with a diameter of 70 cm.

Answer 1

We have given,

For basball,

Diameter of baseball =70cm

(a)

Hence,the approximate speed(v) 5.35m/s at which the linear and quadratic drag forces are equally important.
(b)The velocity which is approximate to treat the drag force as purely quadratic is about less than 5m/s.
(c)For the beach ball,we can ignore the linear term and with a beach ball of diameter 70cm we can answer same as the baseball.