How Far Did the Stuntwoman Fall Based on Doppler Shift Analysis?

[jwbehm]

Homework Statement

A stuntwoman is preparing to take a punch, crash through a "candy glass" window, and fall a long distance. The script calls for her to emit a piercing scream just before she hits the "ground." In reality, she will land on a waiting airbag. Lights! Camera! Action! The primary camera crew, filming from her starting height, hears her last-instant scream at a frequency 3.77 kHz. Her scream has a frequency of 4.05 kHz when she is at rest. How far did she fall? Report this as a positive distance.

Homework Equations

Fl=Fs(v-Vl/v+Vs)

The Attempt at a Solution

I have easily found the speed of the girl falling to be 25.5m/s but I don't even know where to start as far as finding her distance. I have considered finding the wavelength but I don't know where to go from there. Do I need to you an echo equation for this? I've been looking at it for a solid 2 hours convinced I could figure it out but I'm about to the point where I need a little guidance. I don't need an answer I just need an idea of where to go from here. This isn't due for another 3 weeks but its driving me insane.

THANKS!

 

[collinsmark]

Good 'ol kinematics might help. You know g = 9.8 m/s². Assuming her initial position and velocity were both approximately zero, how far would she have to fall to reach the target velocity, when accelerating at g?

[If you don't remember the single, direct equation for this, you can use a couple other kinematics equations. Use one equation to calculate the time it takes to reach the final velocity, then another equation to calculate the distance.]

 

[jwbehm]

I was afraid it would be something like that. . . thanks. I should be able to get it from here but if not ill be back within the next 20 minutes haha

 

[jwbehm]

Wow, that was ridiculously easy. 33.15m. Thanks for the help!

 

[rdl]

I would approach this problem by first understanding the concept of the Doppler effect and how it relates to distance. The Doppler effect is the change in frequency of a wave, such as sound, due to the relative motion between the source of the wave and the observer. In this case, the source of the sound is the stuntwoman and the observer is the camera crew.

Next, I would use the equation Fl=Fs(v-Vl/v+Vs) to relate the observed frequency (Fl) to the emitted frequency (Fs) and the velocities of the source (Vl) and the observer (Vs). From the given information, I can plug in the values for Fl and Fs and solve for the difference between Vl and Vs.

Once I have the difference between the velocities, I can use the fact that the stuntwoman is falling at a constant acceleration of 9.8 m/s^2 to find the time it takes for her to fall. Then, using the equation d=Vot + 1/2at^2, I can calculate the distance (d) she fell.

So, in summary, to find the distance she fell, I would use the Doppler effect equation to find the difference between the velocities of the source and observer, use the constant acceleration of gravity to find the time, and then use the distance formula to calculate the distance.