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

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?

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Xavia 2 weeks 2021-08-31T14:01:43+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-31T14:03:07+00:00

    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=188.65m

    (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

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