Question

In a river there is a constant current of 0.40m/s. A motor boat can move relative to the water at a constant speed of 1.3m/s.

a) Calculate the speed of the boat relative to land when the boat goes upriver
Calculate the speed of the boat relative to land when the boat goes downriver
b) Calculate the speed of the boat relative to land when the boat crosses the river perpendicularly, and how much downstream it moves if the river is 30m wide

Answer 1

a) When the boat goes upriver, it moves against the current. To calculate the speed of the boat relative to land, we need to subtract the current's speed from the boat's speed.

Relative speed of the boat going upriver = Boat's speed - Current's speed

Relative speed = 1.3 m/s - 0.40 m/s

Relative speed = 0.9 m/s

Therefore, the speed of the boat relative to land when going upriver is 0.9 m/s.

When the boat goes downriver, it moves in the same direction as the current. To calculate the speed of the boat relative to land, we need to add the current's speed to the boat's speed.

Relative speed of the boat going downriver = Boat's speed + Current's speed

Relative speed = 1.3 m/s + 0.40 m/s

Relative speed = 1.7 m/s

Therefore, the speed of the boat relative to land when going downriver is 1.7 m/s.

b) When the boat crosses the river perpendicularly, it is moving at an angle relative to the current. To find the speed of the boat relative to land in this case, we can use vector addition.

The speed of the boat relative to land can be calculated using the Pythagorean theorem:

Relative speed^2 = (Boat's speed)^2 + (Current's speed)^2

Relative speed^2 = (1.3 m/s)^2 + (0.40 m/s)^2

Relative speed^2 = 1.69 m^2/s^2 + 0.16 m^2/s^2

Relative speed^2 = 1.85 m^2/s^2

Relative speed = sqrt(1.85 m^2/s^2)

Relative speed ≈ 1.36 m/s

Therefore, the speed of the boat relative to land when crossing the river perpendicularly is approximately 1.36 m/s.