Question

In the 2016 Olympics in Rio, after the 50 m freestyle competition, a problem with the pool was found. In lane 1 there was a gentle 1.2 cm/s current flowing in the direction that the swimmers were going, while in lane 8 there was a current of the same speed but directed opposite to the swimmers' direction. Suppose a swimmer could swim the 50.0 m in 25.0 s in the absence of any current.

Part A: How would the time it took the swimmer to swim 50.0 m change in lane 1?

Part B: How would the time it took the swimmer to swim 50.0 m change in lane 8?

Answer 1

Length of the swim = L = 50 m

Time taken by a swimmer to swim 50 m in absence of any current = T = 25 sec

Speed of the swimmer in absence of any current = V

V = L/T

V = 50/25

V = 2 m/s

Speed of the current in lane 1 = V_c1 = 1.2 cm/s = 0.012 m/s

Speed of the swimmer in lane 1 = V₁

V₁ = V + V_c1

V₁ = 2 + 0.012

V₁ = 2.012 m/s

Time taken to finish the race in lane 1 = T₁

T₁ = L/V₁

T₁ = 50/2.012

T₁ = 24.85 sec

Change in time to swim 50 m in lane 1 = T₁

T₁ = T₁ - T

T₁ = 24.85 - 25

T₁ = -0.15 sec

It would take the swimmer 0.15 sec less to swim 50 m in lane 1.

Speed of the current in lane 8 = V_c8 = -1.2 cm/s = -0.012 m/s

(Negative as it is in the opposite direction of the motion of the swimmer)

Speed of the swimmer in lane 8 = V₈

V₈ = V + V_c8

V₈ = 2 + (-0.012)

V₈ = 1.988 m/s

Time taken to finish the race in lane 8 = T₈

T₈ = L/V₈

T₈ = 50/1.988

T₈ = 25.15 sec

Change in time to swim 50 m in lane 8 = T₈

T₈ = T₈ - T

T₈ = 25.15 - 25

T₈ = 0.15 sec

It would take the swimmer 0.15 sec more to swim 50 m in lane 8.

A) Time taken by the swimmer to swim 50 m in lane 1 would be less by 0.15 sec.

B) Time taken by the swimmer to swim 50 m in lane 8 would be more by 0.15 sec.