Question

In Gru’s underground lab, a 20kg minion falls on to part of garbage disposal chute that consists of twisting and turning slide that is 15m tall and 33 m long that empties at a 12 degrees downward angle in to an incinerator far below. Other minions rush quickly to a bridge scaffold located above and 4m away from the front of the chute and quickly start to lower a rope. How far must the rope lower below the end of the chute in order for the short-armed minion to be able to grab it? Assume the minion experiences an average frictional force of 14N on the chute and starts his slide with a speed of 3m/s.

Answer 1

Since the slide twists and turns, we can use the conservation of energy to find out the velocity with which the minion will exit the slide.

Energy lost due to friction

Energy gained due to potential energy being converted into kinetic energy

Therefore, kinetic energy of the minion as it exits the chute is

We can now use the kinetic energy to calculate the velocity.

Substituting our values,

This velocity will be directed along the chute, which itself is angled at downward.

To find out how far the rope has to be placed, we have to consider the fact that to grab the rope, the minion has to travel the horizontal distance of in the same time it travels the vertical distance to the rope.

Horizontal velocity of the minion

Time taken to travel this distance

Vertical distance it travels in this time under the influence of gravity

Therefore, the rope has to lower than the chute opening.