Galilean transformation

1. The problem statement, all variables and given/known data

In a Summer's day, there's no wind, and start to rain. So the drops fall vertically for an observer on the ground. A car has a velocity of 10 Km/h and the driver see that the drops are coming perpendicularly to the windshield. If 60° is the angle between the windshield and the horizontal, determine:
1) The velocity of the drops seen from the earth.
2) The velocity of the drops when hits the windshield.

2. Relevant equations

[tex]v_D^C[/tex] = velocity of the drop for the driver

[tex]v_C^G[/tex] = velocity of the car for an observer on the ground

[tex]v_D^G[/tex] = velocity of the drop for an observer on the ground

[tex]v_D^G = v_D^C + v_C^G[/tex]

3. The attempt at a solution

[tex]v_D^C = Xcos(330°) \hat{i} + Xsen(330°) \hat{j}[/tex]

[tex]v_C^G = -10 \hat{i}[/tex]

And because the drops are falling vertically:

[tex]Xcos(330°) \hat{i} - 10 = 0[/tex]

[tex]X = 11,55 km/h[/tex]

Then, (1):

[tex]|v_D^G |= Xsin(330) = -5,77 km/h[/tex]

And finally (2):

[tex]|v_D^C| = 11,55 km/h[/tex]

I don't know if it is correct :P

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