Question

A farmer is attempting to take a chicken across a river in a motorboat while a fox waits on shore with a bag of grain. If the river has a current with a velocity of 2.0 m/s and the boat maintains a speed relative to the water of 4.5 m/s, in which direction (angle) should the farmer point the boat so that the boat follows a straight path directly across the river?

Answer 1

The farmer should go approximately 26.39° relative to the direction of and toward the river current velocity or approximate 90 - 26.39 which is 63.12° clockwise from the perpendicular direction across the river

Step-by-step explanation:

The given parameters are;

The river current velocity = 2.0 m/s

The boat speed relative to the water = 4.5 m/s

Therefore, for the boat to have a resultant velocity that will follow a straight path directly across the river, we have;

The water current velocity, 2 m/s, the relative speed of the boat, 4.5 m/s, and the resultant velocity, v, form a right triangle, with the water current being the base, and the boat's relative speed being the hypotenuse side, while the height is the resultant velocity

Therefore, we have;

The direction of the boat relative to the direction of current the river = θ

The relative speed of the boat × sin(θ°) = The river current velocity

∴ sin(θ°) = The river current velocity/(The relative speed of the boat)

Which gives;

sin(θ°) = 2 m/s/(4.5 m/s) = 2/4.5 = 4/9

θ = sin⁻¹ = sin⁻¹(4/9) ≈ 26.39°

Therefore, the farmer should go approximately 26.39° relative to the direction of and toward the river current velocity or approximate 90 - 26.39 which is 63.12° clockwise from the perpendicular direction across the river.