Question

Two persons p and q are standing at a distance of 100 m from a high wall as shown in the figure when p give the clap the time interval between two direct and reflected sound hereby q is 0.2 seconds if the speed of the sound is 340 metre per second then the distance between the p and q is what

Answer 1

$\huge \mathfrak{Question:-}$

Two persons p and q are standing at a distance of 100 m from a high wall as shown in the figure when p give the clap the time interval between two direct and reflected sound hereby q is 0.2 seconds if the speed of the sound is 340 metre per second then the distance between the p and q is what!

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$\huge\underline\red{Solution:-}$

Let say Distance Between P & Q  = d  m

Distance of Wall from P & Q = 100 m

Let say Distance of reflection point on wall from P & Q

✧= a  &  b  m

Reflection at 90°  so a & b are perpependicular

✧=> a² + b² = d²

Also Area of  triangle

✧= (1/2) a * b = (1/2) * d * 100

✧=> ab  = 100d

Difference between reflected and Direct sound = 0.2 sec

Distance covered in 0.2 sec = 340 * 0.2 = 68 m

✧=> a + b =  d + 68

Squaring both sides

✧=> a² + b² + 2ab  = d² + 68² + 136d

using a² + b² = d²   & ab = 100d

✧=> d² + 200d = d² + 68² + 136d

✧=> 64d = 68²

✧=> 4d = 17²

✧=> d = 289/4

✧=> d = 72.25 m

the distance between the P and Q is 72.25 m!!!