Two swimmers of identical ability want to race across a river. The goal is to touch the other side first (anywhere along the bank). Both swimmers can swim at a

Question

Two swimmers of identical ability want to race across a river. The goal is to touch the other side first (anywhere along the bank). Both swimmers can swim at a rate of 5m/s in still water. The river’s current is 3m/s. Swimmer A points upstream so that she ends up travelling straight across the river along a line perpendicular to the point on the shore where she started. Swimmer B points directly across and ends up downstream due to the river’s current.

a. Which swimmer makes it across first? Why do you think this is so?

b. If the river is 50m wide determine the time it takes for each swimmer to cross.

c. Using swimmer B above solve for the following: Construct the equivalent displacement vector diagram and label all sides and angles with correct values. Use the equation d = vt and solve for t in each direction (i.e time to travel downstream, time to travel diagonally).

d. How far downstream does Swimmer B end up?

Answers a)B b)12.5s,10s c)
50m,30m,58m d)30m

Answer 1

a) From the vector diagrams b has a greater resultant velocity across the river and hence would get their first, even his perpendicular velocity is 5m/s compared to (a) which is 4 m/s.

 

b) a takes 50/4 = 12.5 secs; b takes 50/5 = 10 secs

 

c) no way to construct diagram on this software but from the triangle sides = 50m, 30m, and (50² + 30²)^1/2 = 58.3m

    by the way the time taken in each direction is the same 10 seconds.

 

d) Using similar triangles, 3/5 = x/50; from this x = 30m