Question

Two men are standing 800m apart at the same distance from a vertical hillock.one of them fires a shot and other hears a echo,3s after hearing the direct sound. find the distance of the men from the hillock assuming the velocity of sound in air is 340m/s.

Answer 1

Answer: $d_{2} = 918\ m$

Explanation:

Given that,

Distance between the two man is

$d_{1} = 800\ m$

Speed of sound v = 340 m/s

We know that,

The sound of the shot fired reaches directly from first man to the second man and it travels toward the hillock and reflect back to the second man as an echo then, the time will be

$t = \dfrac{d_{1}}{v}$

$t = \dfrac{800\ m}{340\ m/s}$

$t = 2.4\ s$

Now, the echo is heard 3 s after

$t= t_{1} + 2.4\ s$

$t = 3\ s+2.4\s$

$t= 5.4\ s$

Now, the distance between men and hillock

$2d_{2} = v\times t$

$d_{2} = \dfrac{340\ m/s\times5.4\ s}{2}$

$d_{2} = 918\ m$

Hence, the distance of the men from the hillock is 918 m.

Answer 2

Answer:

Given: Distance between the two men = 800 m , v = 340 m/s , distance between the two men from the hillock is same.

Solution:

The time taken (t) for the direct sound to be heard by the other man = d / v

= 800/340 seconds

t = 40/17 seconds

Now, since the other man hears the echo 3s after the direct sound is heard ,

Therefore; total time taken(T) to hear the echo = ( t + 3 ) s

= 40/17 + 3

T = 92/17 seconds

Now;

T = 92/17 s , d (dist. of the two men from the hillock) = ? , v = 340m/s

Therefore;

distance of the two men from the hillock( = distance of one man from the hillock) = vT/2

= (340 × 92/17 × 1/2) m

= 920m (Ans)

Explanation:

920m is the correct answer! 918m is completely wrong! Try not to convert the fraction into decimal places if there is division/multiplication/addition/subtraction ahead because the numbers in the fraction might cut/simplify during these operations which will make your calculations much easier!! This is my tip!