The sled is moving at 11.68 m/s after being towed 18.3 m along the diagonal of the hill.
We can use the work-energy principle to solve this problem. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
The work done by the tension force on the sled is equal to the force times the distance moved. The force is the tension in the rope, which is 252 N. The distance moved is 18.3 m.
The angle of the hill is 17.6°, so the horizontal component of the force is 252 N * cos(17.6°) = 219 N. The work done by the tension force is therefore:
W = 219 N * 18.3 m = 4019.7 J
The change in kinetic energy of the sled is equal to its final kinetic energy minus its initial kinetic energy. The initial kinetic energy of the sled is zero, since it is at rest. The final kinetic energy of the sled is equal to its mass times its speed squared. The mass of the sled is 64.4 kg. Let the final speed of the sled be "v". Therefore, the change in kinetic energy is:
ΔKE = 0.5 * 64.4 kg * v^2
Since the work done by the tension force is equal to the change in kinetic energy of the sled, we can set these two equations equal to each other:
4019.7 J = 0.5 * 64.4 kg * v^2
Solving for v, we get:
v = √(2 * 4019.7 J / 64.4 kg) = 11.68 m/s
Therefore, the sled is moving at 11.68 m/s after being towed 18.3 m along the diagonal of the hill.
Question
A tow rope is used to move a 64.4-kg sled up a ski hill that is inclined at 17.6° above the horizontal. The tension in the toe rope is held constant at 252 N. The rope is aligned parallel to the ski hill. Neglect friction. How fast is the sled moving after being towed 18.3 m along the diagonal of the hill?