A person can swim at a speed of 2 kilometers per hour in still water. If he heads across a river at right angles to current of 5 kilometers per hour, find his speed in relation to the land and the direction in which he actually moves.

speed^2 = 2^2 + 5^2

Θ is the angle downstream from directly across
... tan(Θ) = 2/5

Vr = X + Yi = 2 - 5i = 5.39km/h[-68.2o] = 5.39km/h[68.2o]S. of E.

= Resultant velocity and Direction.

post it.

To find the person's speed in relation to the land and the direction in which he moves, we can use vector addition.

Let's represent the speed of the person in still water as "v1" and the speed of the river current as "v2". The person's speed in relation to the land, also called the resultant velocity, can be found by adding these two vectors.

Given:
Swimming speed in still water (v1) = 2 kilometers per hour
River current speed (v2) = 5 kilometers per hour

To find the resultant velocity, we can use the Pythagorean theorem to calculate the magnitude and trigonometry to determine the direction.

Magnitude of resultant velocity (Speed in relation to land):
Magnitude = sqrt(v1^2 +v2^2)
Magnitude = sqrt(2^2 + 5^2)
Magnitude = sqrt(4 + 25)
Magnitude = sqrt(29)
Magnitude ≈ 5.39 kilometers per hour (rounded to two decimal places)

To determine the direction in which the person moves, we can use trigonometry:
Tan(theta) = (v2 / v1)
Tan(theta) = (5 / 2)
theta ≈ 68.2 degrees (rounded to one decimal place)

Therefore, the person's speed in relation to the land is approximately 5.39 kilometers per hour, and the direction in which he actually moves is approximately 68.2 degrees from the direction in which he started.