A baseball fan sitting in the "cheap seats" is d = 166 m

Question

A baseball fan sitting in the "cheap seats" is d = 166 m

 from home plate (see the figure below). How much time elapses between the instant the fan sees a batter hit the ball and the moment the fan hears the sound? (Assume the speed of sound is 344 m/s, and the vertical distance can be ignored.)

Answer 1

Since we're told that vertical distance can be ignored, we can take the distance between the fan and home plate as 166 meters.

From there, we can use the formula t=x/v, plug in our values for v (344 m/s) and x (d=166 m), and perform the division to get that t=0.483 seconds, cutting off any remaining decimals in accordance with significant figures practice. That gives us the time between when the bat hits the ball and when the fan hears the ball.

To check how long it takes between when the ball is struck and when the fan sees it, we use the same formula, but with the speed of light c=3x10^8 m/s for v, giving us 5.53x10^-7 seconds. Since this is outside of our significant figures, we can disregard this, and give our final answer as t=0.483 seconds, or 4.83x10^-1 seconds (in scientific notation).