How Fast Was the NASCAR Race Car Going?

AI Thread Summary
The discussion centers on calculating the velocity of a NASCAR race car based on the frequency changes observed by spectators. Initially, the frequency heard was 821 Hz, which dropped to half that value after the car passed. Participants note that the correct approach involves using the Doppler effect rather than wave velocity equations. The focus is on understanding how the frequency shift relates to the car's speed as it moves along the +x axis. Accurate application of the Doppler shift principles is essential for determining the car's velocity.
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Homework Statement



George and Martha are at a NASCAR race and as the race car made the turn to their right and rushed towards them the frequency they heard was F0 = G5 or 821 Hz. However, after it passed the frequency dropped to F0/2. The direction the cars are traveling is the +x axis, what is the velocity of the race car?



Homework Equations



Wave velocity = frequency x wavelength
 
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Not the right equation - you are looking for the velocity of the car, not the sound.
Do you know about Doppler shifts?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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