Question

Two people are pulling a boat through the water. Each exerts a force of 600 N directed at a 30.0 angle relative to the forward motion of the boat. If the boat moves with constant velocity, find the resistive force exerted by the water on the boat.

Answer 1

It sounds as though the two people are standing in front of the boat on opposite sides of it, so that they both make an angle of 30.0° with the axis of the boat, as in the attached free body diagram (ignoring the force of buoyancy and the weight of the boat).

By Newton's second law, the net vertical force is

∑ F = P₁ sin(60.0°) + P₂ sin(120.0°) - R = 0

where upward is positive and downward is negative, and the right side is 0 because the boat moves with constant velocity and thus zero acceleration.

We're told that P₁ = P₂ = 600 N, and we know sin(60°) = sin(120°), so the above reduces to

R = 2 P sin(60.0°) = 2 (600 N) sin(60.0°) ≈ 1040 N