In this worksheet, we will practice calculating the drag force acting on objects moving at various speeds through various fluids.

**Q2: **

A skydiver with a mass of
80.0 kg
falls through air that has a uniform density of 1.23 kg/m^{3}.
The skydiver has a surface are of 0.140 m^{2} and a drag coefficient of 0.690.
What is the skydiver’s terminal velocity?

**Q3: **

A boater and motor boat are at rest on a lake. Together, they have mass kg. The thrust of the motor provides a constant force on the boat of 40 N in the direction of the boat’s motion. If the value of resistive force of the water in Newtons is two times the value of the speed of the boat in m/s, find the limiting speed of the boat.

**Q4: **

A spherical raindrop of radius m has a density of kg/m^{3}. The drag coefficient of the raindrop is 0.450 as it falls through air of density 1.225 kg/m^{3}. What is the difference in the final vertical downward speed that the raindrop reaches after starting from rest and falling 4.22 km if drag forces acting on it are neglected and if they are not neglected?

**Q5: **

The terminal velocity of a 48.7-kg-mass skydiver is 55.5 m/s. Assuming that drag force can be approximated by , find .

**Q6: **

A small diamond of mass 10.0 g drops from a swimmer’s earring and falls through the water, reaching a terminal velocity of 2.0 m/s.

Assuming the frictional force on the diamond obeys , what is ?

How far does the diamond fall before it reaches 90 percent of its terminal speed?

**Q7: **

Two skydivers simultaneously jump from an aeroplane that is at an altitude of m. Both skydivers have a drag coefficient of 1.00 and their frontal areas are both 0.566 m^{2}. The density of the air through which the skydivers fall is uniformly equal to 1.225 kg/m^{3}. At an altitude of m, the skydivers open their parachutes. The time taken for the skydivers to achieve their terminal velocities is assumed to be negligible compared to their total fall time.

One of the skydivers has a mass of 81.4 kg. How much time will pass between him leaving the aeroplane and opening his parachute?

- A 52.4 s
- B 11.8 s
- C 88.0 s
- D 67.3 s
- E 98.0 s

The other skydiver has a mass of 68.6 kg. How much time will pass between her leaving the aeroplane and opening her parachute?

- A 73.3 s
- B 98.0 s
- C 67.3 s
- D 52.4 s
- E 104 s

**Q8: **

A squirrel of mass 560 g falls
5.0 m
vertically downwards from rest,
out of a tree. The squirrel has a surface area of 930 cm^{2}
and a drag coefficient of 1.0.
The air that the squirrel falls through has a density of 1.2 kg/m^{3}.
At the same time, a man falls out of the tree from the same height.

What is the squirrel’s terminal velocity?

- A 13 m/s
- B 11 m/s
- C 14 m/s
- D 9.9 m/s
- E 16 m/s

What will be the vertical velocity of the man when he hits the ground, assuming that drag forces are negligible?

- A 9.9 m/s
- B 15 m/s
- C 13 m/s
- D 8.2 m/s
- E 19 m/s

**Q9: **

A car has a frontal area of 2.10 m^{2} and a drag coefficient of 0.583. The car drives through air of density 1.225 kg/m^{3}.

The car drives at a velocity of 62.1 km/h. What is the magnitude of the drag force on the car?

The car drives at a velocity of 90.4 km/h. What is the magnitude of the drag force on the car?

**Q10: **

A car has a frontal area of 0.722 m^{2}
and a drag coefficient of 0.216. The car drives through air of density
1.225 kg/m^{3}.

The car drives at a velocity of 62.1 km/h. What is magnitude of the drag force on the car?

The car drives at a velocity of 90.4 km/h. What is magnitude of the drag force on the car?

**Q11: **

A spherical bacterium has a radius of m and its density is kg/m^{3}. The bacterium’s drag coefficient is 0.450. The bacterium falls through water
of density kg/m^{3}. What is the terminal velocity of the bacterium?

- A m/s
- B m/s
- C m/s
- D m/s
- E m/s

**Q12: **

A skydiver is at an altitude of m. After 10.0 seconds of free fall, he opens his parachute and finds that the air resistance is given by the formula , where and is the velocity. The mass of the skydiver is 82.0 kg.

Find the speed of the skydiver when the parachute opens.

Find the distance fallen before the parachute opens.

Find the terminal velocity after the parachute opens.

Find the time the skydiver is in the air after the parachute opens.

**Q13: **

A 70.0 kg swimmer starts a race with an initial velocity of 1.25 m/s and exerts an average force of 80.0 N backward with his arms during each 1.80 m long stroke. The resistance from the water is initially 45.0 N.

What is his initial acceleration?

What is the subsequent average resistance force from the water during the 5.00 s it takes him to reach his top velocity of 2.50 m/s?

**Q14: **

Two skydivers, a man and a woman, jump from an aircraft and
fall until they each reach terminal velocity. The man has a mass
of 85 kg and the woman has a mass
of 50 kg and they both have
a frontal area of 0.70 m^{2} and
a drag coefficient of 1.0.
The air that they fall through has
a mass of 1.21 kg/m^{3}.

What is the man’s terminal velocity?

What is the woman’s terminal velocity?

**Q15: **

The resistive force exerted by the air on a skydiver of mass 100 kg can be modelled as . If the skydiver’s terminal velocity is 60 m/s, what is the value of ?

- A 2.6 kg/m
- B 3.7 kg/m
- C 1.5 kg/m
- D 0.27 kg/m
- E 0.72 kg/m

**Q16: **

Two tugboats are pushing a barge from different directions.
The first tugboat exerts force
in the -direction and the second tugboat exerts
force
in the -direction.
The barge has a mass of kg
and it accelerates at m/s^{2}.

What is the magnitude of the drag force exerted on the barge?

- A N
- B N
- C N
- D N
- E N

At what angle below the negative -direction is the drag force on the barge directed?