Sound waves and the doppler effect

[seb26]

Homework Statement

A jet is flying horizontally from A to B. When the plane is directly overhead at B, a person on the ground (C) hears the sound coming from A. ABC is a right triangle in B. The angle BCA = 36 degrees.
The average temperature is 20 degrees Celsius. If the speed of the plane at A is 170 m/s, what is the speed at B, assuming that it has constant acceleration?

Homework Equations

f=1/T f: frequency; T: period
v= λ*f = λ/T λ: wavelength
f_observer= f_plane*((v+v_o)/(v+v_p)) v=343m/s

The Attempt at a Solution

First off I don't see what steps to take to come up with the answer. There must some implicit data to take into consideration but I can't figure it out.
What I assume, since there is a right triangle with an angle given, is that one distance has to be found (AC) to find AB with sin.
I found the acceleration by taking t=1second. I know that the sound travels at 343m/s on AC and the speed the plane has after one second on AB is found by calculating v_plane= sin(36)*343= 201.6m/s so the acceleration is a= (201.6-170)/1s= 31.6m/s²
I can't figure out how to get the distance from A to C or A to B.

PS: those values are given from my homework given by the teacher, on the book the same problem has 164m/s for the speed of the plane at A, same angle. The answer for the speed at B is 239m/s

 

[rl.bhat]

Hi seb26, welcome to PF.
your relevant equations are irrelevant, because the problem is not based on Doppler effect.
It is just kinematic equation.
If vi is the initial velocity of the jet at A, vs is the velocity of the sound and t is the time taken by the jet to travel from A to B, then
AB = vi*t + 1/2*a*t^2 ...(1)
Sound starting form A takes the same time t to reach C. So
AC = vs*t...(2)
AB/AC = sinθ...(3) And vf - vi = at...(4)
Using above hints find the velocity of the jet at B.

 

[Riaz44]

After a whole day of trying to crack this problem with my buddy, your advice is what led us to the answer. God bless you and those of you who help students like us out.

Peace,

Riaz