15. You are watching a baseball game on television that 15

being broadcast from 4500 km away. The batter hits

the ball with a loud "crack" of the bat. A microphone

is located 22 m from the batter, and you are 2.0 m from

the television set. On a day when sound travels 343 m/s

in air, what is the minimum time it takes for you to hear

the crack of the bat after the batter hits the ball?

It asks us how long it takes to hear the sound, for this we must look for the time (t₁) it takes for the sound to reach the microphone, the time it takes for the video signal (t₂) to reach the television and the time (₃) it takes for the TV sound to reach us, so the total delay time is

t_total = t₁ + t₂ + t₂

we look for t1, it indicates that the distance x = 22m

v = x / t

t = x / v

t₁ = 22/343

t₁ = 6.41 10-2 s

time t₂

t₂ = 4500 103/3 108

t₂ = 1.5 10-5 s

time t₃

t₃ = 2/343

t₃ = 5.83 10⁻³

Total time is

t_total = t₁ + t₂ + t₃

t_total = 6.41 10⁻² + 1.5 10⁻⁵ + 0.583 10⁻²

t_total = 6.99 s