# Find the velocity of the rain with respect to the car and the Earth

tubworld
I would like to confirm the answer to this question.

A car travels due east with a speed of 50.0 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 75.0° with the vertical. Find the velocity of the rain with respect to the car and the Earth.

Thanx.

GDogg
You mean relative motion :tongue2:

You have 3 frames of reference: one attached to the rain, another one to the car and the last one to the Earth. Using Galilean Transformations and basic trigonometry you should be able to solve it...

GDogg said:
You mean relative motion :tongue2:

You have 3 frames of reference: one attached to the rain, another one to the car and the last one to the Earth. Using Galilean Transformations and basic trigonometry you should be able to solve it...

You don't even need any Transformations, just use trigonometry. You can construct a right angled triangle.

Regards,

Homework Helper
I'd solve this in the car's frame of reference. The vertical component of the raindrop velocity is the same for the car and earth. So you just have to figure out the horizontal component. It's not that hard.

tubworld
unsure still. horizontal component or vertical

I tried. But which is which? Is the horizontal component the speed relative to the car or the what?
pls help! I really suck at this!

Homework Helper
tubworld said:
I tried. But which is which? Is the horizontal component the speed relative to the car or the what?
pls help! I really suck at this!
In the frame of reference of the earth, the velocity vector for the rain is directed vertically downward. If you are in the frame of reference of the car, the rain appears also to be moving horizontally rearward at 50 km/hr. So it appears to have its vertical velocity plus a horizontal velocity of 50 km/hr in the rearward direction. You have to find the magnitude of the vertical vector such that, when added to the rearward horizontal vector, results in a vector that has a direction that is 75 degrees to the vertical (15 degrees below the horizontal).

AM