Question

When Ben swam across the Maumee River, the current carried him 350 yards downstream from his starting point. If the river is 375 yards wide, how far did Ben swim?

Answer 1

By using the given information, we can calculate the distance that Ben swam is 40 meters.

Step-by-step explanation:

To solve this problem, we can use the concept of relative velocity.

The swimmer is swimming perpendicular to the water current, so the speed of the swimmer with respect to the ground is the vector sum of the swimmer's speed and the water current's speed.

Let's say the speed of the water current is Vc and the speed of the swimmer with respect to the water is Vs. The speed of the swimmer with respect to the ground is given by the formula:

V = √(Vs2 + Vc2)

In this case, the swimmer's speed with respect to the water is 0.5 m/s and the swimmer reaches a point 40 m downstream.

Using the given information, we can calculate the speed of the water current:

40 = (0.5 m/s + Vc) * t

where t is the time taken to cross the river. Solving for t, we find:

t = 80 s

Substituting the value of t into the equation, we can solve for Vc:

40 = (0.5 m/s + Vc) * 80 s

Vc = 0.5 m/s

Therefore, the speed of the water current is 0.5 m/s.

Now, we can use this information to calculate the distance Ben swam:

Distance = Speed * Time

Distance = 0.5 m/s * 80 s

Distance = 40 meters