A stunt rider plans to jump a motorcycle across a canyon
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A stunt rider plans to jump a motorcycle across a canyon. The takeoff point is the edge of a cliff that is 50.0 m above the canyon floor. The landing ramp on the opposite side is 35.0 m horizontally from the cliff edge and 15.0 m below the takeoff point. Immediately after leaving the edge, the rider can tilt the motorcycle so that its velocity vector makes an angle θ above the horizontal while maintaining the same speed v0. Ignore air resistance and take g=9.8m/s2.
(a) Derive a single equation involving tanθ that must be satisfied for the motorcycle to land on the start of the ramp. Show all algebraic steps.
(b) Solve the equation from part (a) to find the numerical value(s) of θ that permit a successful landing.
(c) For each value of θ obtained in part (b), determine the minimum launch speed v0 required.
(d) If the motorcycle can achieve a maximum speed of 25.0 m/s, identify which launch angle(s), if any, are physically attainable and justify your answer.