I'm stumped by this one and my engineer flatmates weren't any help.
Someone is attempting to jump a 100m canyon on his motorbike. the ramp is inclined at 30degrees and the top of the ramp is level with the ground on the other side of the canyon.
By assuming that the man and his bike is a point mass and there's no wind resistance, it can be shown that the flight path taken by the man's bike is a parabola
where g=10ms^-2 is the gravitation constant, and v his launch speed (in ms^-1.
Use the arc length formula to write down a definite integral which gives the lengh of the flight path in terms of v. then evaluate the integral to get an expression for the arc length in terms of v.
I played with it for a while with not much luck. I think I have to parametrize the equation into something like x=vcos(30)t, y=vsin(30)t -(1/2)gt^2 then use the parametric arc length formula. Then there's the trig substitution to worry about, i guess it'll be something substituted for tan then integrating sec. Any help would be wonderful.