Aman stand btn 2 clift and fires agun ,he hears the first echo after the 2 second and the second echo after 3/2 second.caculate the distance between the 2clift

Physics

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Answer

600. m600.\ \text{m}

Step-by-step solution

4 steps

To calculate the distance between the two cliffs, we need to determine the distance of the man from each cliff and then sum these distances. We will assume the speed of sound in air.

  1. State the assumed speed of sound

    The speed of sound in dry air at 20∘C20^\circ\text{C} is approximately v=343 m/sv = 343\ \text{m/s}.

  2. Calculate the distance to the first cliff

    The first echo is heard after t1=2 st_1 = 2\ \text{s}. The sound travels to the cliff and back, covering twice the distance to the cliff.
    Let d1d_1 be the distance to the first cliff.
    2d1=v×t12d_1 = v \times t_1
    d1=v×t12d_1 = \frac{v \times t_1}{2}
    d1=343 m/s×2 s2d_1 = \frac{343\ \text{m/s} \times 2\ \text{s}}{2}
    d1=343 md_1 = 343\ \text{m}

  3. Calculate the distance to the second cliff

    The second echo is heard after t2=32 s=1.5 st_2 = \frac{3}{2}\ \text{s} = 1.5\ \text{s}.
    Let d2d_2 be the distance to the second cliff.
    2d2=v×t22d_2 = v \times t_2
    d2=v×t22d_2 = \frac{v \times t_2}{2}
    d2=343 m/s×1.5 s2d_2 = \frac{343\ \text{m/s} \times 1.5\ \text{s}}{2}
    d2=514.5 m2d_2 = \frac{514.5\ \text{m}}{2}
    d2=257.25 md_2 = 257.25\ \text{m}

  4. Calculate the total distance between the two cliffs

    The total distance between the two cliffs, DD, is the sum of the distances from the man to each cliff.
    D=d1+d2D = d_1 + d_2
    D=343 m+257.25 mD = 343\ \text{m} + 257.25\ \text{m}
    D=600.25 mD = 600.25\ \text{m}

    Rounding to three significant figures (based on the speed of sound), the distance is 600. m600.\ \text{m}.

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