The baseball player in center field is playing approximately 310 feet from the television camera that is behind home plate.A batter hits a fly ball that goes to the wall 400 feet from the camera (see figure).The camera turns 10° to follow the play.Approximately how far does the center fielder have to run to make the catch?
A)102.9 ft
B)114.9 ft
C)108.9 ft
D)113.9 ft
E)103.9 ft

Question

The baseball player in center field is playing approximately 310 feet from the television camera that is behind home plate.A batter hits a fly ball that goes to the wall 400 feet from the camera (see figure).The camera turns 10° to follow the play.Approximately how far does the center fielder have to run to make the catch? ​  ​
A)102.9 ft 
B)114.9 ft 
C)108.9 ft 
D)113.9 ft 
E)103.9 ft

Quizplus · Accepted Answer

We can use trigonometry to solve for the distance the center fielder has to run.

First, we can find the angle that the ball makes with respect to the camera (since the camera turns 10° to follow the play):

angle = 90° - 10° = 80°

Next, we can find the horizontal distance between the ball and the center fielder using the cosine of the angle:

cos(80°) = adjacent/hypotenuse 
adjacent = hypotenuse * cos(80°) 
adjacent = 400 ft * cos(80°) 
adjacent = 82.46 ft

Finally, we can use the Pythagorean theorem to find the distance the center fielder needs to run:

distance = sqrt(310^2 + 82.46^2) 
distance = 108.9 ft

Therefore, the answer is choice C) 108.9 ft.

The Baseball Player in Center Field Is Playing Approximately 310