Finding the Angle of Rainfall for a Driving Car

[burton95]

Homework Statement

Rain is falling vertically at a constant speed of 8 m/s. At what angle (in degrees) from the vertical will the rain appear to be falling as viewed by a driver traveling on a straight, level road with a speed of 50 km/h?

Homework Equations

vr,c = vr,g + vc,g

The Attempt at a Solution

I set v_r,g = -8, and v_c,g = 13.88 m/s after conversion. I came up with a 13.88 sinθ - 8 = 0. θ = 35.19. 35.19+90 = 125.19. 180 - 125.19 = 54.8 degrees off of vertical. Not even close.

 

[haruspex]

13.88 sinθ - 8 = 0

By what reasoning do you arrive at that?

 

[burton95]

My book had a similar problem. The reasoning was to get the another angle besides the 90° and then i could subtract the difference

 

[burton95]

From 180°

 

[HallsofIvy]

Essentially you have a right triangle with one leg of length and the other of length 13.8. tangent= opposite side/near side.

 

[burton95]

Right I get that but I have a negative number as per my definition of up being positive. I understand -1tan = 13.8/8 but I'm at a loss as to how this would work as I assigned it a value of -8...wait do I just use 8 as the magnitude and "-" is the direction so I only need the magnitude of the velcoity?

 

[haruspex]

Right I get that but I have a negative number as per my definition of up being positive. I understand -1tan = 13.8/8 but I'm at a loss as to how this would work as I assigned it a value of -8...wait do I just use 8 as the magnitude and "-" is the direction so I only need the magnitude of the velcoity?

You can do it either way - just work with magnitudes and figure out the direction separately, or understand that the tangent function goes negative in the second and fourth quadrants (tan(x) = - tan(π-x)).