Chapter 8 Problems
1. When Grant fully exhales, he has a body density of 1.02 g/cm3 (1020 kg/m3). During a
triathlon swim, Grant wears a wetsuit and his density thus decreases to 0.99 g/cm3 (990
kg/m3). The water he swims in has a density of 1.00 g/cm3 (1000 kg/m3).
a. If he fully exhales, can Grant float in the water if he doesn’t wear a wetsuit?
b. If he fully exhales, can Grant float in the water if he does wear a wetsuit?
2. K-1 whitewater kayak has a volume of 225 liters (0.225 m3) and a mass of 10 kg. Sean
wonders if the kayak is big enough for him to use. Sean’s mass is 70 kg. What percent of
the kayak will be submerged when Sean sits in it? Assume that the water density is 1.00
g/cm3 (1000 kg/m3).
3. Marathon swimmer DJ is swimming in the Atlantic Ocean. She is moving north with a
velocity of 2 m/s relative to the water. The ocean current is also moving north but at 1
m/s. What is DJ’s absolute or true velocity?
4. Lily is sprinting in a 100 m dash. At the 80 m mark her velocity is 9.5 m/s. She is running
into a 3 m/s headwind. What is the velocity of the air relative to Lily?
5. Carter is running a 400 m race around a 400 m track. On the backstretch his velocity is 8
m/s, but he is running into a 2 m/s headwind. How large is the drag force that acts on
Carter? Assume that the density of the air is 1.2 kg/m3, that Carter’s cross-sectional area
is 0.5 m2, and that the coefficient of drag for Carter is 1.1.
6. During the 400 m race in question 5, Carter is now in the homestretch. His velocity is still
8 m/s, but he now has a 2 m/s tailwind. How large is the drag force acting on Carter
now? Assume that the density of the air is 1.2 kg/m3, that Carter’s cross-sectional area is
0.5 m2, and that the coefficient of drag for Carter is 1.1.
7. Amy and Josh are coasting on their bicycles down a 10° slope at 15 m/s through still air.
The mass of Amy and her bicycle is 60 kg. The mass of Josh and his bicycle is 90 kg. The
cross-sectional area of Amy and her bicycle is 0.45, while the cross-sectional area of Josh
and his bicycle is 0.60. The drag coefficient for both cyclists is 0.70. Other than gravity
and air resistance, the external forces acting on the two bicycle and rider systems are
the same. Which cyclist is more affected by air resistance?
8. When Paul rides his bicycle at 5 m/s, the drag force acting on him and his bicycle is 6 N.
If he speeds up to 10 m/s, how large will the drag force become?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).