Question

A baseball player in center field is approximately 310 feet from a television camera that is behind home plate. A batter hits a fly ball that goes to the wall 420 feet from the camera (see figure). The camera turns 6° to follow the play. How far (in ft) does the center fielder have to run to make the catch? (Round your answer to one decimal place.)

Answer 1

To find the distance the center fielder has to run to make the catch, we can use trigonometry. Since the camera turns 6° to follow the play, we can consider the camera's view as a right triangle. The distance the center fielder has to run will be the hypotenuse of this triangle.

Using the given measurements, the distance from the camera to the wall is 420 feet, and the distance from the camera to the center fielder is 310 feet. We can use the tangent function to find the length of the hypotenuse.

tan(6°) = (opposite side) / (adjacent side)
tan(6°) = x / 310

Solving for x, the distance the center fielder has to run, we get:
x = tan(6°) * 310

Calculating this value, the center fielder has to run approximately 32.4 feet to make the catch.