A swimmer heads directly across a river, swimming at 1.5 m/s relative to the water. She arrives at a point 30 m downstream from the point directly across the river, which is 87 m wide.

Question

A swimmer heads directly across a river, swimming at 1.5 m/s relative to the water. She arrives at a point 30 m downstream from the point directly across the river, which is 87 m wide.

(c) In what direction should the swimmer head so as to arrive at the point directly opposite her starting point?

Answer 1

Did you see Sheenybeany's response?

http://www.jiskha.com/display.cgi?id=1407609411

Answer 2

First crossing:

time to cross = 87/1.5 = 58 seconds
so speed of current = 30/58 = .517 m/s

second crossing
v upstream = 1.5 sin A = .517
sin A = .345
A = 20.2 degrees

then if they ask:
v across = 1.5 cos A

Answer 3

To determine the direction in which the swimmer should head to arrive directly opposite her starting point, we need to consider the velocity of the river's current as well as the swimmer's velocity relative to the water.

Let's break down the problem:

1. The river's width is given as 87 m.
2. The swimmer's velocity relative to the water is given as 1.5 m/s.
3. The swimmer ends up 30 m downstream from the point directly across the river.

First, let's calculate the time it took for the swimmer to cross the river. We can use the formula:

time = distance / velocity

The distance the swimmer has to swim cross the river is the width of the river, which is 87 m. Therefore, the time taken to cross the river is:

time = 87 m / 1.5 m/s = 58 s

Now, let's consider the distance the swimmer is displaced downstream during this time. We can use the formula:

distance downstream = velocity of the current × time

Since the swimmer is displaced by 30 m downstream, we can rearrange the formula to solve for the velocity of the current:

velocity of the current = distance downstream / time

velocity of the current = 30 m / 58 s ≈ 0.52 m/s

So, the velocity of the river's current is approximately 0.52 m/s.

To determine the direction in which the swimmer should head, we need to add these velocities vectorially. Draw a vector representing the swimmer's velocity relative to the water and another vector representing the current's velocity. The swimmer should head in the direction opposite to the vector sum of these two velocities, i.e., the resultant vector.

By subtracting the velocity of the current from the swimmer's velocity relative to the water, we can determine the direction the swimmer should take to arrive directly opposite her starting point.