Relative Velocity: Car & Rain w/ Respect to Earth

[changzv]

A car travels due east with a speed of 55.0 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 70.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.

(a) the car in m/s

(b) the Earth in m/s


I have converted the speed of the car from km/h to m/s which is

v=(55x1000)/3600
=15.278m/s

I have no idea where to start.. Please guide me..
Does the horizontal motion have no relation to the vertical motion therefore velocity of the rain with respect to the car = 15.278m/s?
Thanks in advanced!

 

[jbsteele]

Yes, the horizontal motion of the car has no relation to the vertical motion of the rain, so the velocity of the rain with respect to the car is 15.278 m/s. To find the velocity of the rain with respect to the Earth, you will need to use the trigonometric relationship between the angle of 70 degrees and the velocity of the rain. Specifically, you can use the cosine law to calculate the magnitude of the vertical component of the rain's velocity. Let v_r be the velocity of the rain with respect to the Earth. Then you have:v_r^2 = (15.278)^2 + v_y^2 - 2*15.278*v_y*cos(70°)Solving for v_y gives:v_y = (15.278^2 + v_r^2)/(2*15.278*cos(70°))From this, you can calculate the velocity of the rain with respect to the Earth.