Speed at the top of the ramp?

Question

If Evil Kneival drives his motorcycle up a ramp (inclined 30 degrees above the horizotal) and sails over 10 buses (spanning 36 meters) and lands on a similar ramp, what was his speed at the top of the ramp (either one)?

Answer 1

First, compute the time it takes to travel horizontally from one ramp to the next:

Cos(30)*vi*t>=36

And the velocity in the vertical will be zero in half the flight time to land exactly on the edge of the ramp

sin(30)*vi=g*t/2

so
t=sin(30)*2*vi/g

substitute into the original equation

Cos(30)*vi*sin(30)*2*vi/g>=36
Cos(30)*sin(30)*2*vi^2/g>=36

vi>=sqrt(36*g/(Cos(30)*sin(30)*2))

vi>=20.2 m/s

To land exactly at the tip of the opposite ramp, ignoring air resistance,
vi=20.2 m/s

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