An iceboat is at rest on a frictionless frozen lake?

Question

An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 212 N, toward east, on the boat. Due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 7.0 m in a direction 20° north of east.
(a) What is the kinetic energy of the iceboat at the end of that 7.0 m?
kJ
(b) The boat has a mass of 300 kg. What is the speed of the boat?
m/s

Answer 1

Physics books come up with dumb problems sometimes, and this is a doozy. If there really were an eastward force on the sail and no other forces, the boat would move east. The description of an angle sail doesn't help. Force on a sail is due to pressure, and pressure on a surface always acts perpendicularly to the surface...of the sail, in this case. If that force is eastward, then the sail must be perpendicular to east (aka north-south) and there is no 20 degree anything in the problem.

Still, you have to solve it, presumably by guessing what they want. The only force that contributes to work is the component in the direction of motion, which is 20 deg N of E. Assume that the 20 deg N of E force is a component of some imaginary eastward 212N force. This has a magnitude of (212 N)*cos(20) in the direction of motion, so the work done by this force over the 7m is
W = (212 * cos(20) * 7) joules.

Since there is no friction, K = W

The velocity is an easy solve from K = (1/2)mv^2