Question

A person standing at a distance x in front of a cliff fires a gun. Another person B standing behind the person A at a distance y from the cliff hears two sounds of the fired shots after 2s and 3s respectively. Calculate x and y(take speed of sound 320m/s)


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Answer 1

Explanation:

Given speed of sound = 320 m / s

Time taken by the sound to reach from A to B directly

Speed =

d

i

s

t

a

n

c

e

t

i

m

e

320 =

y

–

x

2

Or, y – x = 320 × 2

Or, y – x = 640 ----- (i)

After reflection from the cliff

320 =

y

+

x

3

Or, y + x = 320 × 3

Or, y + x = 960 ----- (ii)

By adding equation (i) and (ii)

2y = 1600

y =

1600

2

= 800 m

Now, substituting y in eq (i)

y – x = 640

Or, 800 - x = 640

Or, x = 160 m

∴ x = 160 m and y = 800 m.

Answer 2

Given: A person standing at a distance x in front of a cliff fires a gun. Another person B standing behind person A at a distance y from the cliff hears two sounds of the fired shots after 2s and 3s respectively.

To find: The values of x and y.

Solution:

• The distance of person A from the cliff is x and the distance of person B from the cliff is $(x+y)$.
• The first time person B heard the sound of the fired shot, it was directly from the gun.
• Distance can be calculated using the following formula.

        $distance = speed * time$

• In the given question, y is the distance of person B from the gun and the time taken is 2 seconds.

        $y = 320ms^{-1} * 2s$

           $= 640 m$

• When person B hears the fired shot for the second time, the sound has reached the cliff from person A and then echoed back to person B in 3 seconds.
• So, the distance travelled by the sound is,

        $x + (x + y) = 2x + y$

• Now, the value of y is calculated as,

        $distance = speed * time$

        $2x + y = 320ms^{-1} * 3s$

        $2x + 640 m = 320ms^{-1} * 3s$

        $x = 160 m$

Therefore, the value of x is 160 m and the value of y is 640 m.