Question

A swimmer who can swim at 5 m/s relative to the water wishes to travel due south across a river. The current in the river is 3 m/s[E]. [A /2 marks] a. What heading must the swimmer take to make it directly across the river?

Answer 1

To travel directly across the river, the swimmer must take a heading that accounts for the current. The swimmer should head in a direction approximately 30.96° south of east.

Step-by-step explanation:

To travel directly across the river, the swimmer must take a heading that accounts for the current. This can be found using vector addition. The velocity of the swimmer relative to the ground is the vector sum of the swimmer's velocity relative to the water and the velocity of the water relative to the ground. Since the swimmer is moving directly south and the current is flowing directly east, the swimmer needs to compensate by heading slightly south of east. The angle can be calculated using trigonometry.

Using the Pythagorean theorem, we can determine the magnitude of the swimmer's velocity relative to the ground:

5 m/s2 + 3 m/s2 = v2

v = √(5 m/s)2 + (3 m/s)2

v ≈ 5.83 m/s

The angle can be determined using the arctangent function:

θ = arctan(3 m/s / 5 m/s)

θ ≈ 30.96°

Therefore, the swimmer should head in a direction approximately 30.96° south of east to make it directly across the river.