Question

John was swimming in the river. His swimming velocity was 1.2 m/s due east. The water was running at 0.4 m/s due west. John’s projected area in the water was 0.45 m2. Water density was 1000 kg/m3. The coefficient of drag was 0.2. (a) What was John’s velocity relative to the water? (b) What was the pressure drag force from the water? After a little while, John turned around and now is swimming at 1.2 m/s due west. (c) What is John’s velocity relative to the water now? (d) What is the pressure drag force from the water now? (e) What is the percentage of change in pressure drag force?

Answer 1

a) when John is moving due east 1.2 m/s

      water velocity   due west = 0.4 m/s

John velocity relative to water = 1.2 + 0.4 = 1.6 m/s

b) Drag Force

F_d = 1/2 u²C_d A

density of water = 1000 kg/cu.m

velocity relative to water u = 1.6 m/s

drag co-efficient C_d = 0.2

projected Area A = 0.45 sq.m

F_d = 0.5*1000*1.6²*0.2*0.45 = 115.2 N

c) John's velocity   1.2 m/s due west

             water velocity = 0.4 m/s due west

        velcoity relative to water = 1.2- 0.4 = 0.8 m/s

d) drag Force F_d = 0.5 *1000*0.8²*0.2*0.45

                                = 28.8 N

e) percent change = (115.2 -28.8)*100/115.2 = 75%