PROBLEM:

Q1: In the sport of field hockey, a “stick stop” or “vertical stick stop” is a skill in which a player uses their stick — held straight up, such that the front, flat surface-edge side of the stick is perpendicular to the ground — and aligns the stick with the motion of an incoming ball moving toward the player with an initial positive velocity, in order to use their stick to stop and control the ball, and thus change the direction of play.

Players of different positions on the field often look to purchase a stick composed of different types of material, depending on which position they play. Some players want to be able to hit a ball the fastest, to drive it in the opposite direction down the field.

Other players want to be able to stop an incoming ball with the greatest amount of control possible — that is, for an incoming ball to hit their stick, and bounce off of it with as little of a final velocity in the opposite direction as possible, so that the ball will land as close to the player as possible, following the ball/stick collision.

Q2: A sports equipment manufacturing company is testing two field hockey sticks, composed of different materials. They are testing the two sticks by shooting an identical ball at each of the sticks, which each then stop the ball, allowing it to bounce off of the front, flat surface edge-side of the stick.

The testers use sensors to measure the “force profile” between the incoming balls and each of the two sticks: the force profiles are represented as graphs with respect to time — Force (F, in kN) vs. time (t, in ms). The results for each collision are shown in the graphs.