Question

A person hears the sound of a jet aeroplane after it has passed over his head.The angle of the jet plane with the horizontal when the sound appears to be coming vertically downward is 60°.If the velocity of sound is C then find the velocity of jet plane.​

Answer 1

Answer:

velocity of jet plane = C/2

Explanation:

A person hears the sound of a jet aeroplane after it has passed over his head.The angle of the jet plane with the horizontal when the sound appears to be coming vertically downward is 60°.If the velocity of sound is C then find the velocity of jet plane.​

Angle of Jet Plane = 60°

Let say Distance between Man & Jet plane = D

Then Horizontal Distance between man & Jet = D Cos60 = D/2

Distance traveled by sound = D

Speed of Sound = C

Time Taken = D/C

Distance covered by Jet = D/2

Time Taken = D/C

Speed = (D/2)/(D/C)  = C/2

velocity of jet plane = C/2

Answer 2

Given as :

The angle of the jet plane with horizontal when sound appears to be coming vertically downward = 60°

The velocity of sound = C  m/s²

To Find :

The velocity of Jet plane

solution :

Let The velocity of Jet plane = S  m/s²

Let The Distance between person & jet plane = D  meters

Now,

The horizontal distance = D cos 60°

I.e                                     = D × $\dfrac{1}{2}$

∴  The horizontal distance = $\dfrac{D}{2}$  meters

Again

Distance traveled by sound =Distance between person & jet plane = D m

i.e  Distance traveled by sound = D meters

And Speed of Sound = C

∵ Time = $\dfrac{Distance}{Speed}$

Or, Time taken by sound = $\dfrac{D}{C}$  sec

Again

Since , The horizontal distance cover by jet = $\dfrac{D}{2}$  meters

And Time by Jet plane to cover $\dfrac{D}{2}$   distance = Time taken by sound

i.e  Time taken by Jet plane cover $\dfrac{D}{2}$  = $\dfrac{D}{C}$  sec

∵ Speed = $\dfrac{Distance}{Time}$

Or,  Velocity of jet plane = $\dfrac{Distance cover to sound}{Time taken by sound}$

i.e S = $\dfrac{\dfrac{D}{2} }{\dfrac{D}{C} }$

Or,  S = $\dfrac{C\times D}{D\times 2}$

∴  Velocity of Jet plane = S = $\dfrac{C}{2}$  m/s

Hence, The Velocity of Jet plane is $\dfrac{C}{2}$  m/s  . Answer