Question

Two spectators at a soccer game see, and a moment later hear, the ball being kicked on the playing field. The time delay for the spectator A is 0.55 s, and for the spectator B it is 0.45 s. Sight lines from the two spectators to the player kicking the ball meet at an angle of 90°. The speed of sound in the air is 343 m/s.

How far are (a) spectator A and (b) spectator B from the player?
(c) How far are the spectators from each other?

Answer 1

a)188.65m

b)154.35m

c)243.7m

Step-by-step explanation:

Given data:

`t_A=0.55s`

`t_B=0.45s`

(a) The distance from the kicker to each of the 2 spectators is given by:

`d_A=v * t_A`

where,

v= speed of sound

`t_A`=time taken for the sound waves to reach the ears

`d_A=343* 0.55=188.65`m

(b)
`d_B=v * t_B`

where,

v= speed of sound

`t_B`=time taken for the sound waves to reach the ears

`d_B=343* 0.45=154.35m`

(c)As the angle b/w slight lines from the two spectators to the player is right angle,

hypotenuse=the distance b/w 2 spectators

and, the slight lines are the other 2 lines

`D^2=d_A^2+d_B^2\\D=√(188.65^2+154.35^2) \\D= 243.7m`