Calculating the Physics Behind Super-Bouncy Shoes

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In summary: As for the "shoe context", you can consider the person as a projectile launched at an angle, with the initial speed calculated from the distance and the acceleration due to gravity. The only difference between a person and a cannonball is the shape and mass distribution, which would affect the air resistance, but that can be neglected as stated in the problem. So the same equations of motion apply.In summary, the conversation discusses the calculation of the minimum initial speed and time taken for a person wearing super-bouncy shoes to cover a distance of 100 metres in one leap, neglecting air resistance. The problem is similar to shooting a person out of a cannon, and the equations of motion for a projectile can be used to solve it. However
  • #1
quarktacular
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Suppose a person who wears a pair of super-bouncy shoes is able to cover a distance of 100 metres with one leap. Calculate the
a) minimum initial speed he/she would have to achieve
b) time taken for him/her to complete his/her leap with the above speed
(Neglect air resistance.)



Homework Equations





The answer to the initial speed question is most probably unrealistic as it is humanly impossible to complete a 100 metre leap of that sort. I'm lost for an answer so any help would be greatly appreciated. Thanks!
 
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  • #2
quarktacular said:
it is humanly impossible to complete a 100 metre leap of that sort.
Yea, the shoe thing is kinda dumb.
Calculate the a) minimum initial speed ... b) time taken
You should also find the jumping angle that corresponds to the minimum initial speed. This is a classic artillery problem.

Work out the equations of motion for both axes; solve them at the landing point; eliminate time from the equations; convert to polar coordinates; solve for the initial speed; differentiate with respect to the jumping angle; and find where the derivative is zero.
 
  • #3
Welcome to PF!

Hi quarktacular! Welcome to PF! :smile:
quarktacular said:
Suppose a person who wears a pair of super-bouncy shoes is able to cover a distance of 100 metres with one leap. Calculate the
a) minimum initial speed he/she would have to achieve
b) time taken for him/her to complete his/her leap with the above speed
(Neglect air resistance.)

mmm … it's the same question as "suppose you want to shoot a person out of a cannon 100 metres …" :wink:

happier now? :smile:​
 
  • #4


tiny-tim said:
Hi quarktacular! Welcome to PF! :smile:


mmm … it's the same question as "suppose you want to shoot a person out of a cannon 100 metres …" :wink:

happier now? :smile:​

Thanks for the welcome! Happier that at least someone gave the question a try but the thing is, it's not the same question. Trust me, it's not. My teacher keeps on telling me that it's do-able in the shoe context but seriously, I really don't know how he does it.
 
  • #5


quarktacular said:
Trust me, it's not.

Trust us - it is. It is the same combination of initial angle and speed.
 

FAQ: Calculating the Physics Behind Super-Bouncy Shoes

How do you calculate the bounciness of a shoe?

The bounciness of a shoe can be calculated by measuring the coefficient of restitution, which is the ratio of the height of a bouncing object after impact to its initial height. This can be determined by dropping the shoe onto a hard surface and measuring the height of its bounce.

What factors affect the bounciness of a shoe?

The bounciness of a shoe can be affected by several factors, including the materials used in the sole and upper, the design and structure of the shoe, and the amount of air or other cushioning elements present.

Can the bounciness of a shoe be increased?

Yes, the bounciness of a shoe can be increased by using materials with higher elastic properties, such as rubber or foam. The design and structure of the shoe can also be optimized for maximum bounce.

How does the physics behind bounce affect super-bouncy shoes?

The physics behind bounce plays a crucial role in the design and function of super-bouncy shoes. By understanding the principles of elasticity and energy transfer, scientists can develop shoes that can maximize bounce and provide a greater level of comfort and performance for the wearer.

Are there any potential drawbacks to super-bouncy shoes?

While super-bouncy shoes can provide enhanced performance and comfort, there are potential drawbacks to consider. These include a higher risk of injury due to increased impact forces, as well as a shorter lifespan of the shoes due to the strain placed on the materials from repeated bounces.

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