Question

To be rescued from the roof of a burning building, a62-kg man must be able to jump straight up and catch hold of a rope ladder hanging from a helicopter. He has to raise his center of mass2.00 m above the roof to do so.

If he crouches down such that his center of mass is 0.50 m above the roof and his feet leave the roof when his center of mass is 1.05 m above the roof, what minimum force must he exert on the roof to reach the ladder?

A typical candy bar contains about Ecandy = 900 kJ of food energy. How many candy bars does this jump require?

Answer 1

Hello
Well, first we're going to raise the exercise so that we can resolve it with work and energy (at least the first part)

It is a leap we can consider the following:
will be mechanical energy all the way, so we use the formula that expresses the relation between work and energy

where

is Delta mechanical energy

  is the work of non-conservative forces

as the person jumps, not "friction force" is in any part of the route and the air resistance is not taken into account. so the work of non-conservative forces equals 0

considering that at the time the jump, the center of mass is not placed on the ground so that in that intant, there is kinetic energy and potential energy. once reached the yfinal kinetic energy would not exist, so

and final expression would be

to understand a little more about the delta Y, we will observe the following picture

where Y1 is the distance center of mass to the ground,at the time that this bent (Y1 = 0.5m). and yfinal is the height to which you want to reach the center of mass for so saved (yfinal = 2m)

Once the speed, we will use kinematics to find the acceleration of the person, using the following formula

But in order to determine the force necessary apply Newton's first law

so the value of the force applied by the person to the ground in order to reach salvation is 405.48N

for the second part will be necessary to evaluate the mechanical energy of the jump

solving

and now we will establish relation between the amount of candy bar with the energy equivalent

would be necessary