Representation of the wave crests

AI Thread Summary
The discussion revolves around calculating the Doppler shift of a siren sound as heard by Jim, who is driving through an intersection while an ambulance is at rest in traffic. Initially, the user struggled with the problem but later realized the error was due to miscalculating the vector component. The correct Doppler shift was determined to be 0.229 kHz. The user expressed gratitude for the assistance, indicating they resolved the issue independently. Overall, the focus was on understanding the Doppler effect in this specific scenario.
mexqwerty
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I've been trying to do the following question but I can't get the right answer. Also, I put in the wrong thread title but I don't know how to change it (sorry).

An ambulance is at rest in a traffic jam in front of an intersection. At that moment, Jim is driving his car at 88.0 km/h through the intersection as shown in the diagram below. In the diagram, the angle θ = 59.0 °.

What is the doppler shift (Δf = f′–f) heard in the siren sound by Jim, when Jim and the ambulance are positioned as shown on the diagram above? The answer is 0.229 kHZ.
 

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Never mind. I got the answer. I was just calculating the wrong vector component. Thanks for looking, anyway.
 
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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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