# 100 metre leap

#### quarktacular

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.)

2. 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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#### danb

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.

#### tiny-tim

Homework Helper
Welcome to PF!

Hi quarktacular! Welcome to PF!
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 …"

happier now?

#### quarktacular

Re: Welcome to PF!

Hi quarktacular! Welcome to PF!

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

happier now?
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.

#### Borek

Mentor
Re: Welcome to PF!

Trust me, it's not.
Trust us - it is. It is the same combination of initial angle and speed.

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