Question

A man fires bullets at two hillocks, one shorter and the other taller. The taller one is behind the smaller one. If the first echo is heard after 6 s and the second echo after 12 s, then the distance between the hillocks is (velocity of sound in air = 330 m/s):

• A. 660 m
• B. 990 m
• C. 1320 m
• D. 500 m
• E. 860 m

Hint:

The distance to the hillocks can be calculated by using the time for the sound to travel to the hillock and back. Since the sound travels both to and from the hillock, divide the total distance by 2.

Answer 1

The Correct Option is B

When the bullet is fired, two echoes are heard:

• The first echo after \( 6 \) seconds is from the shorter hillock.
• The second echo after \( 12 \) seconds is from the taller hillock.

The distance traveled by sound in time \( t \) is given by:

\[ d = v \times t \]

where:

• \( v = 330 \) m/s is the velocity of sound in air.
• \( t \) is the time taken for the sound to travel to the object and back.

For the shorter hillock:

• Total time for the sound to travel to the shorter hillock and return: \( t_1 = 6 \) s.
• Distance traveled by sound: \[ d_1 = v \times t_1 = 330 \times 6 = 1980 \, \text{m} \]
• Distance to the shorter hillock: \[ d_{\text{short}} = \frac{1980}{2} = 990 \, \text{m} \]

For the taller hillock:

• Total time for the sound to travel to the taller hillock and return: \( t_2 = 12 \) s.
• Distance traveled by sound: \[ d_2 = v \times t_2 = 330 \times 12 = 3960 \, \text{m} \]
• Distance to the taller hillock: \[ d_{\text{tall}} = \frac{3960}{2} = 1980 \, \text{m} \]

Thus, the distance between the two hillocks is:

\[ \text{Distance between hillocks} = d_{\text{tall}} - d_{\text{short}} = 1980 - 990 = 990 \, \text{m} \]

Therefore, the distance between the hillocks is:

\[ \boxed{990 \, \text{m}} \]