Question

a student wants to climb to the top of a building. if his rope is massless, the hook weighs 2 kg, and the building is 9 meters tall and the rope is 1 meter above the ground, what is the minimum velocity the rope must be thrown at to reach the top of the building?

b.) What is the minimum force the student must use?

c.) The student can't get down from the top, so people set up a balloon pillow at the bottom of the building. If the pillow is 1 meter tall, what is the minimum force the balloon must exert on the student to prevent him from hitting the ground?

Answer 1

a) The rope is thrown vertically, its displacement is given by:

On the other hand the minimum velocity would be that for wich the top position is reached with zero speed, therefore:

Replacing backwards:

b) The minimum force the student must use must be:

c) Before hitting the pillow the students falls 8 m, his speed at that moment is:

The desceleration must be such that:

The force balance on the student gives:

Where m is the mass of the student