## Question on Heat, Pressure, and Doppler's Effect

1. The problem statement, all variables and given/known data
I have 310g mass 24°C Water and I add 85g of 0°C ice.

What is the final temperature after the ice melted and come to equilibrium?

2. Relevant equations
I think its Q=mcΔt
with a mix of Q=mL

3. The attempt at a solution
I have no idea.

1. The problem statement, all variables and given/known data
I have density of air of 1.2 kg/m³. Air pressure at earth surface 1.01x10^5 Pa. I need to find the height of the atmosphere.

2. Relevant equations
P=pgh

3. The attempt at a solution
So I made the problem; 1.01x10^5=(1.2kg/m³)(9.8m/s)(height) and found for height and got 8588.435m. Is that right? I don't know what a "believable" answer would look like.

1. The problem statement, all variables and given/known data
This is suppose to be a scenario where the police is using a radar to find the speed of passing cars. So, the velocity is in EM (speed of light). There is a note that says there are two Doppler shifts so I use a squared version of the formula. The Radar is bounced off the moving cars and the Doppler-shifted frequency of the echo's signal is compared to the frequency of the original signal.

The microwave frequency of 1.4x10^9 Hz is used for the original signal and the reflected signal is 350 Hz lower than that. (the car is moving away from the radar gun). What is the speed of the car in mph?

Hint: there are two Doppler shifts

2. Relevant equations
freflected = (Vw/(Vw+Vcar))² f original

3. The attempt at a solution

(1.4x10^9)-350 Hz = (3x10^8/(3x10^8+X)²(1.4x10^9)

There is something I'm missing but I dunno. I solve the [I]f[/I]reflected and divide by f original. I then square root both sides and divide Vw by freflected and solve for X

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