You want to swim straight across a river that is 76m wide. You find that you can do this if you swim 28 degrees upstream at a constant rate of 1.7m/s relative to water. At what rate does the river flow? The angle is measure from the river bank (directly upstream is 0 degrees while directly across the river is 90 degrees.

Question

You want to swim straight across a river that is 76m wide. You find that you can do this if you swim 28 degrees upstream at a constant rate of 1.7m/s relative to water. At what rate does the river flow? The angle is measure from the river bank (directly upstream is 0 degrees while directly across the river is 90 degrees.

Answer 1

The answer will not depend upon the width of the river. That number is there to confuse you.

To swim straight across, the swimmer's "relative to water" velocity component in the upstream direction must equal the river's speed downstream. Let the swimming angle relative to water, and the river bank, be A. Let the swimmer's velocity relative to water be v = 1.7 m/s.

v cos A = 1.7 cos 28 = V
V = 1.50 m/s

Answer 2

WHAT IS PHYSICS

Answer 3

To find the rate at which the river flows, we can use the concept of vector addition.

Let's assume the rate at which the river flows is represented by vector R, and the rate at which you swim is represented by vector S.

We know that the resultant vector (representing your actual motion across the river) is a straight line from your starting point to your ending point.

Since you are swimming at an angle of 28 degrees upstream, it means that your swimming vector S is at an angle of 28 degrees with the river bank.

To find the resultant vector, we can split vector S into two components: one component parallel to the river's flow and one component perpendicular to the river's flow.

The component parallel to the river's flow is given by S_parallel = S * cos(28°).

The component perpendicular to the river's flow is given by S_perpendicular = S * sin(28°).

Now, the resultant vector is the sum of the vector representing the river's flow (R) and the component parallel to the river's flow.

We can write this as: R + S_parallel = S.

Since we want to find the rate at which the river flows, let's denote that as V.

Now, we can write the equation as: V + S_parallel = S.

Substituting in the values: V + S * cos(28°) = S.

Simplifying the equation: V = S - S * cos(28°).

Given that S = 1.7 m/s, we can calculate V as follows:

V = 1.7 m/s - 1.7 m/s * cos(28°).

Using the cosine value for 28 degrees, which is approximately 0.882, we can calculate V.

V = 1.7 m/s - 1.7 m/s * 0.882 ≈ 1.7 m/s - 1.498 m/s ≈ 0.202 m/s.

Therefore, the rate at which the river flows is approximately 0.202 m/s.

Answer 4

To find the rate at which the river flows, we need to analyze the situation using trigonometry.

Let's assume that the rate at which the river flows is denoted by "v" m/s.

When swimming upstream at an angle of 28 degrees, the component of your velocity perpendicular to the river's flow is given by v * sin(28). This component is responsible for countering the river's flow and enables you to swim straight across the river.

Since you are able to swim straight across the river, we can equate the component of your velocity perpendicular to the river's flow with the river's flow velocity itself.

v * sin(28) = v

Now, we can solve this equation to find the value of "v."

Dividing both sides of the equation by v gives us:

sin(28) = 1

However, there is no angle for which the sine function equals 1. Therefore, we cannot find a value for "v" that satisfies this equation.

From this analysis, we can conclude that swimming with a velocity of 1.7 m/s at an angle of 28 degrees upstream is not sufficient to swim straight across the river.