Relative Motion Question Involving Rain and Moving Car

AI Thread Summary
A car is moving east at 45.0 km/h while rain falls vertically, creating a 45.0° angle on the windows. The velocity of the rain relative to the car is calculated to be 17.7 m/s using trigonometry, though there was confusion about the sign. For the rain's velocity relative to the Earth, the correct approach involves separating the horizontal and vertical components of the velocities. The final calculation shows that the rain's vertical velocity is 12.5 m/s downward. The discussion emphasizes the importance of treating the velocity vectors correctly in both components.
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Homework Statement


A car travels due east with a speed of 45.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 45.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.
(a) the car

(b) the Earth


Homework Equations


n/a


The Attempt at a Solution


I managed to find the answer of part a) which is 17.7 m/s using simple trigonometry although I didn't really understand why the sign was positive.
I found the velocity of the car to be 12.5 m/s and with my diagram got:
sin45=12.5/Vr (Vr= velocity of rain relative to the car)
Vr = 12.7 m/s

For part b, I thought that
velocity of rain relative to car = velocity of car relative to Earth - velocity of rain relative to earth
So, 17.7 = Vre -12.5
So I found the velocity of rain relative to the Earth to be 30.2 m/s.

I can't remember where I got that reasoning for part b from, but is that the only thing that's wrong?

Please help...
 
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ff_yy said:
I managed to find the answer of part a) which is 17.7 m/s using simple trigonometry although I didn't really understand why the sign was positive.
The sign just depends on your coordinate system; all they want is the magnitude of the velocity.
I found the velocity of the car to be 12.5 m/s and with my diagram got:
sin45=12.5/Vr (Vr= velocity of rain relative to the car)
OK.
Vr = 12.7 m/s
?? Typo?

For part b, I thought that
velocity of rain relative to car = velocity of car relative to Earth - velocity of rain relative to earth
Not exactly. Instead:
velocity of rain relative to car + velocity of car relative to Earth = velocity of rain relative to earth
So, 17.7 = Vre -12.5
No. Realize that the equation above is a vector equation. Apply it to each component separately.
 
So, when you say apply the vector equation to each component separately, can I split say the vector of velocity of rain relative to car into horizontal and vertical components?

And that would mean that
horizontally: Vre= -12.5 +12.5 = 0
vertically: vre =12.5 + 0 = 12.5

So answer is just 12.5 m/s (down)

If that's not right, then I'm not sure what you mean...
 
You got it.
 
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