Some physics problems (4)

Problem:

Kevin Bania has created chaos online with his new video on youtube. From standing position, he jumps 162.5 centimeters above the ground.

Physics Professor Rhett Alain user Banias record jumps to say something about gravity (weight point is the same as the point of attack for gravity) and how it affects resilience. Allain provides an estimate of where the gravity to Bania is located (stomach area) and calculates how high of a record the man actually jumped. The answer is 86 cm, the rest of the 162,5 cm retrieves Bania gets when he pulls his legs up under himself

a) Add the zeropoint for potential energy in Banias gravity and assume Bania has a mass of 75 kg. Show that the rise in potential energy is 0, 63 KJ

b) From the video it takes ca.1.2 seconds to do the jump. What is the theoretical minimum worth we may have for effect at a displacement on 86 cm?

c) will the answer in b) be a realistic measurement for a real jump? Discuss simplifications and idealizations that underlie the calculation.

Solution:

Part a)

The potential energy change is $ mgh = 75 \times 9.8 \times 0.86 = 632.1 J = 0.63 KJ $.

Part b)

With some clarification, we actually wanted the minimum force to achieve the height.

To calculate that, we have a sketch of the v-t  graph as such

At this point, we do not know the actual y-values, the x-values are accurate. At the initial point we have an sudden change in velocity still to the jump, once he leave the ground however, he cannot exert any force and then driven by gravity. The drop part is similar, he receive a collision impact with the ground, and eventually stop.

The area of the left triangle should be the height he jumped, so we have $ \frac{1}{2} v_{max} \times 0.6 = 0.86 $, solving get $ v_{max}= 2.87... ms^{-1} $.

Assuming it take 0.01s second to leave the ground (the usual impact time), the acceleration is $ \frac{2.87}{0.01} = 286.67 $, the force is $ 75 \times 286.67 = 21,500 N $.

Part c)

No, the value above simply does not make sense at all. A few thousand Newton's is what an extreme person can deliver. 21,500N is simply mission impossible.