if a swimmer can swim in still water at a speed of 7.3 m/s and he intends to swim across a river that has a downstream current of 2.5 m/s what is the swimmers direction?
If θ is the angle upstream, then you have
sinθ = 2.5/7.3
To determine the swimmer's direction, we need to consider the velocity of the swimmer and the velocity of the river current. The swimmer's direction can be calculated using vector addition.
1. First, let's assign a positive direction for the downstream current. Since the swimmer intends to swim across the river, we can consider the perpendicular direction to the current as the swimmer's intended direction.
2. The swimmer's velocity relative to still water can be calculated by subtracting the velocity of the river current from the swimmer's velocity in still water. In this case, the swimmer's velocity relative to still water is 7.3 m/s - 2.5 m/s = 4.8 m/s.
3. The swimmer's direction is perpendicular to the downstream current, so we can use the Pythagorean theorem to find the resultant velocity.
4. The magnitude of the resultant velocity can be calculated as the square root of the sum of the squares of the swimmer's velocity relative to still water and the velocity of the river current. In this case, the magnitude of the resultant velocity is √(4.8^2 + 2.5^2) ≈ 5.48 m/s.
5. Finally, to determine the direction of the swimmer, we need to find the angle between the resultant velocity vector and the positive direction selected for the downstream current. We can use the inverse tangent function to find this angle. In this case, the angle is approximately tan^(-1)(2.5/4.8) ≈ 28.6 degrees.
Therefore, the swimmer's direction is at an angle of approximately 28.6 degrees to the perpendicular direction of the downstream current.