r/theydidthemath • u/Persian_Frank_Zappa • 7h ago

[Request] A longboarder hit 94 mph going downhill. If there were a ramp at the bottom, how high could he launch?

Saw this post about a downhill longboarder hitting 94 mph: https://www.reddit.com/r/longboarding/s/ZyF6DmaYCF

What if someone built a ramp at the bottom of that hill and he just kept going? How high could a person actually launch above the ground?

What kind of ramp would it have to be? I'm picturing something like a quarter pipe, but I've also seen those big straight wedge ramps, and ski jumps that curve and then go straight. Does the shape matter a lot at that speed, or is a ramp a ramp?

How big would it need to be? I assume if the curve is too tight he just gets flattened into the ramp.

How steep should the end be if you want max height? Straight up seems like the obvious answer but that also seems like a terrible idea.

How high would he actually go?

Assume he's a serious athlete in good shape, standing on a regular longboard with no bindings, and he wants to go as high as possible and survive the launch.

0 Upvotes
  • permalink
  • reddit

33% Upvoted

3 comments sorted by

•

u/AutoModerator 7h ago

General Discussion Thread

This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

2

u/Appropriate-Falcon75 6h ago

94mph = 42m/s, and we will assume that we want to get maximum height, so the top of the ramp is vertical.

Using v2 = u2 + 2as, we have v=0 at the top, u = 42, a = -9.8.

Solving for s gives s= 90m

Note that assumes all the energy is put into going upwards, and there is no air resistance.

I'm not sure about the optimal shape, but if we want to restrict our athlete to about 6g, it would need to take about 1s to change direction and so would be 42m long. So, if your half pipe was a quarter circle, it would have a circumference of about 160m, or a radius of 25m.