3. (a) The time for the sound to travel from the kicker to a spectator is given by d/v,wheredis the
distance and vis the speed of sound. The time for light to travel the same distance is given by d/c,
where cis the speed of light. The delay between seeing and hearing the kick is ∆t=(d/v)−(d/c).
The speed of light is so much greater than the speed of sound that the delay can be approximated
by ∆t=d/v. This means d=v∆t. The distance from the kicker to the first spectator is
d1=v∆t1= (343m/s)(0.23 s) = 79 m. The distance from the kicker to the second spectator is
d2=v∆t2= (343 m/s)(0.12 s) = 41 m.
(b) Lines from the kicker to each spectator and from one spectator to the other form a right triangle
with the line joining the spectators as the hypotenuse, so the distance between the spectators is
D=d2
1+d2
2=(79 m)2+(41m)
2=89m.