Motorcycle Safety

Classical Mechanics Level 2

A person, of mass $m$ , traveling on an indestructible motorcycle, of mass $M$ , at a constant speed of $v$ collides elastically with an indestructible car that is not moving; what is the furthest this person will land from the motorcycle?

Details and Assumptions:

To make the problem easier assume there is no resistance and disregard the possible height difference between the feet and the ground.
Assume the motorcyclist launches at an angle $\theta = \pi/4$ .

x_{ f }=\frac { M^{ 2 }v^{ 2 } }{ gm^{ 2 } }

x_{ f }=\frac { v^{ 2 } (M+m) }{ gm}

x_{ f }=\sqrt { \frac { (M+m)v }{ gm } }

x_{ f }=\frac { Mv }{ gm }