A man is moving downward on an inclined plane (θ=37)with constant velocity v0 and rain drops appear to him moving in horizontal direction with velocity 2v0 towards him. Find the velocity of the rain.

Answer 1

How the rain appears to the man can be found using the following equation:

V_appears = V_rain - V_man

Or

V_man + V_appears = V_rain

Now we'll make a VLAXY table to visualize this more easily

We'll assume the man is traveling in the positive x direction. We know the velocity of the man is v₀ and hes traveling at an angle of - 37 degrees. We'll use sin and cos to break the vector into x and y coordinates.

The velocity that the rain appears in 2v₀ in the horizontal direction. Because the rain appears to be moving towards the man and the man is traveling in the positive x direction, the rain appears to be traveling in the negative x direction or an angle of 180 deg

Vector | Length | Angle | X coordinate | Y coordinate

-----------------------------------------------------------------------------------------------------

V_man | v₀ | -37deg | v₀ cos -37 | v₀ sin -37

V_appears | 2v₀ | -180deg | -2v₀ | 0

V_rain | | | |

The x coordinate of the rain's velocity equals v₀ cos -37 - 2v₀ since when you add vectors you add up their coordinates.

The y coordinate of the rain's velocity equals v₀ sin -37 + 0 = v₀ sin -37

Vector | Length | Angle | X coordinate | Y coordinate

-----------------------------------------------------------------------------------------------------

V_man | v₀ | -37deg | v₀ cos -37 | v₀ sin -37

V_appears | 2v₀ | -180deg | -2v₀ | 0

V_rain | | | v₀ cos -37 - 2 v₀ | v₀ sin -37

Now with the x and y coordinates of the rain's velocity, you can use trig to get the magnitude and the angle of the rain's velocity