A bicyclist coasting along a road at speed \(v\) collides with a grasshopper flying in the opposite direction at the same speed. The grasshopper sticks to the bicyclist's helmet. Make a sketch showing \((a)\) the two velocity vectors and the two momentum vectors before the collision,

(b) the velocity and momentum vectors after the collision, and

(c) the velocity change and the momentum change for the bicyclist and for the grasshopper.