Question

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

The following information may help you answer this question: 1) The radar gun works by sending a “radar” signal (on a straight line) in the direction that it is pointed. The signal then bounces off 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 is used to determine ball velocity. 2) You may look online for the term “cosine effect” in the context of a radar gun.

a. From a purely biomechanical standpoint, explain the limits to her strategy.

b. Give a mathematical example that illustrate the limitations.

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

Answer 1

The radar gun works by sending out a radio signal in a narrow beam, then receive the same signal back after it bounces off the target object. If the object is moving toward or away from the gun, the frequency of the reflected radio waves when they come back is different from the transmitted waves (this is the Doppler´s effect). From that difference, the radar speed gun can calculate the speed of the object from which the waves have been bounced. This speed is given by the following equation:

where c is the speed of light, f is the emitted frequency of the radio waves and Δf is the difference in frequency between the radio waves that are emitted and those received back by the gun. This equation holds only when object speeds are low compared to that of light.

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Radar gun is designed to measure speed in relation to the internal antenna on the unit. It is most accurate when the ball is traveling directly at the unit. On the other extreme, if the ball is traveling at a 90 degree angle to the radar unit, you would never get any closer to it, so it would not display anything, regardless of ball´s speed. The ideal position for Celeste would be directly in front of the ball.

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