# Relative velocity problem

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1. Sep 22, 2015

### Mr Davis 97

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
$\vec{v_{AC}} = \vec{v_{AB}} + \vec{v_{BC}}$

3. 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?

2. Sep 22, 2015

### RJLiberator

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?