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

Answer:

a)188.65m

b)154.35m

c)243.7m

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:

$d_A=v \times t_A$

where,

v= speed of sound

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

$d_A=343\times 0.55=188.65$m

(b)$d_B=v \times t_B$

where,

v= speed of sound

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

$d_B=343\times 0.45=154.35m$

(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

$D^2=d_A^2+d_B^2\\D=\sqrt{188.65^2+154.35^2} \\D= 243.7m$