# Galilean transformation

#### jdefrancesco

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

$$v_D^C$$ = velocity of the drop for the driver

$$v_C^G$$ = velocity of the car for an observer on the ground

$$v_D^G$$ = velocity of the drop for an observer on the ground

$$v_D^G = v_D^C + v_C^G$$

3. The attempt at a solution

$$v_D^C = Xcos(330°) \hat{i} + Xsen(330°) \hat{j}$$

$$v_C^G = -10 \hat{i}$$

And because the drops are falling vertically:

$$Xcos(330°) \hat{i} - 10 = 0$$

$$X = 11,55 km/h$$

Then, (1):

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

And finally (2):

$$|v_D^C| = 11,55 km/h$$

I don't know if it is correct :P

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