Question

Asked Nov 13, 2019

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Estimate Timothy Goebel's initial takeoff speed, initial rotational velocity, and initial angular momentum when he performs a quadruple lutz. Goebel's mass is about 55 kg and the height of the jump is about 0.64 m, Note that his angular speed will change quite a bit during the jump, as he begins with arms outstretched and then pulls them in. Your answer should be accurate to within a factor of 2, if you are careful. (We assume that we can model him as a 2.0-m long cylindrical with an average radius of 0.15 m and a mass of 55 kg. We also assume that he launches himself at an angle of 45° with the horizontal with his spread wide, and then pulls them in to increase his rotational speed during the jump. We finally assume that he can change his moment of inertial by a factor of 2 by pulling his arms in.)

Step 1

Use the third kinematic equation to establish a relation between his initial takeoff speed *v _{o}* and the maximum elevation reached by him denoted as

Step 2

The vertical component of the velocity *v _{oy}* is related to the initial velocity

*v _{oy}= v_{o}*sin 45 ͦ

For vertical motion, it is known that,

*a _{y }*= -

The final velocity *v *at maximum elevation is zero.

Use the above substitutions in the third kinematic equation and calculate the initial velocity *v _{o} *as,

Step 3

Goebel’s total air launch time *ta *will be twice the time taken by him to reach maximum elevation.

Thus the time taken ...

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