# Problem: A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance (from A to C) is 200 m, the distance (from C to B) is 150 m , and the speed of the current in the river is 5 km/hr . Suppose that the swimmer's velocity relative to the water makes an angle of θ = 45° with the line from A to C, as indicated in the figure.To swim directly from A to B, what speed, relative to the water, should the swimmer have?(Express the swimmer's speed numerically, to three significant figures, in kilometers per hour)As for the figure, it is a right triangle consisting of points A, B, and C. C to B lie on the x-axis and the distance from C to B is labeled "d2". A to C lies on the y-axis and the distance from A to C (point zero) is "d1". Angle θ = 45° and lies at point A.

###### FREE Expert Solution

Let the angle between AB and AC be Φ.

tan Φ = 150/200 = 3/4

The velocity of the water is (5,0)

The y-component of  net velocity is:

vy = uscosθ

The x-component of net velocity is:

vx = 5 - ussinθ

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###### Problem Details
A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance (from A to C) is 200 m, the distance (from C to B) is 150 m , and the speed of the current in the river is 5 km/hr . Suppose that the swimmer's velocity relative to the water makes an angle of θ = 45° with the line from A to C, as indicated in the figure.
To swim directly from A to B, what speed, relative to the water, should the swimmer have?
(Express the swimmer's speed numerically, to three significant figures, in kilometers per hour)
As for the figure, it is a right triangle consisting of points A, B, and C. C to B lie on the x-axis and the distance from C to B is labeled "d2". A to C lies on the y-axis and the distance from A to C (point zero) is "d1". Angle θ = 45° and lies at point A.

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Our tutors have indicated that to solve this problem you will need to apply the Relative Velocity in 2D concept. You can view video lessons to learn Relative Velocity in 2D. Or if you need more Relative Velocity in 2D practice, you can also practice Relative Velocity in 2D practice problems.