1.                            Celeste Orion, an assistant coach for The Vanishing Planet SoccerTeam has been asked to evaluate each of the team’s players todetermine which players kick with the highest velocity. Celesteborrows a radar gun from her friend Pluto. She gathers the playerstogether and asks them to stand at the penalty mark and kick theball into the goal as hard as they can. She tells them that theball must go into the goal for it to be considered “legal”. Shestands, dead center behind the goal, holds the radar gun 4 ft offthe ground and points it directly at the penalty mark (slightlydownward). She gives each player 3 “legal” kicks and records thehighest speed.

The following information may help you answer this question: 1)The radar gun works by sending a “radar” signal (on a straightline) in the direction that it is pointed. The signal then bouncesoff the object and returns (on a straight line) back to the gun.The change in the rate of the signal return to the radar gun isused to determine ball velocity. 2) You may look online for theterm “cosine effect” in the context of a radar gun.

a. From a purely biomechanicalstandpoint, explain the limits to her strategy.

b. Give a mathematical example thatillustrate the limitations.

c. Identify a simple strategy (orstrategies) that she might use to improve her analysis.