Jonny Alpha, Daredevil
Jonny Alpha regularly performs stunts for his adoring fans. Their favourite trick is his famous ‘10 bus leap’. However, on this occasion, his archrival Billy Beta sets out to try and steal the show. He plans to perform the jump at the same time as Jonny, approaching from the opposite direction and jumping over Jonny by a small amount ....
You are to advise Billy on how much faster he must be travelling, when he leaves the ramp, in order to clear his rival safely.
Answer the following:
- What approach speed is required to jump over 10 buses?
- Is this an achievable speed?
- What angle would you suggest for the ramp?
- What is your advice to Billy?
State any assumptions you make. What are the main limitations of the model?
Hint
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Solution
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Solution
- We can calculate the take off speed that A needs to clear 10 buses (approx 2.5m wide each - so the range, R, of A’s jump must be at least 25m). That speed is then approximately 16 ms-1 (about 60 kmh).
- The maximum range is achieved with a take-off ramp at 45 degrees. Let’s assume that both take-off and landing ramps are set at this angle.
- The only way therefore that B can avoid A is to follow a different trajectory; the trajectory equation tells us that the only was to do this if the ramp angle (and presumably g!) is the same for A and B, is to go faster.
- A possible strategy is to use the trajectory equation to find the
coordinates of A’s highest point of flight :
assuming a coordinate origin at the point of A’s take-off.
- We then need to ensure that B’s trajectory goes through a point safely above this - let’s say (12.5, 8.5). We then use these coordinates as inputs to the trajectory equation for B, and solve for his take-off speed. (Which is calculated to be approximately 19 ms-1).
- Note that B will make a much longer jump than A: you can calculate B’s range and determine the coordinates of the point of maximum height for him.
- You’re left to sort out the issue of who sets off when.....
- And did anyone think about the wind that is often (always?) blowing....?