# Relative velocity problem

• Mr Davis 97

## Homework Statement

A person looking out the window of a stationary train notices that rain drops are falling vertically down at a speed of 5.0 m/s relative to the ground. When the train moves at a constant velocity, the raindrops make an angle of 25° when they move past the window. How fast is the train moving?

## Homework Equations

##\vec{v_{AC}} = \vec{v_{AB}} + \vec{v_{BC}}##

## The Attempt at a Solution

T = train, R = rain, G = ground
##\vec{v_{TG}} = \vec{v_{TR}} + \vec{v_{RG}}##
##\vec{v_{TG}} = \vec{v_{RG}} - \vec{v_{RT}}##
##v_x = 0~m/s-[(5~m/s)\sin25^{\circ}] = 2.1131~m/s##
##v_y = (-5~m/s) -[(5~m/s)\cos25^{\circ}] = -0.468~m/s##
##\vec{v_{TG}} = \sqrt{(2.1131~m/s)^2 + (-0.468~m/s)^2} = 2.16~m/s##

However, according to the solution manual, the correct answer is 2.3 m/s. Where am I going wrong?

Try drawing a right triangle.

The vertical length is the trains speed.
The horizontal length is the rain drop speed of 5.0.

Which angle are you looking from?