# Math Help - mechanics

1. ## mechanics

A railway wagon of mass 12 tonnes moving freely at 4m/s collides with an empty stationary wagon of mass 4 tonnes at the base of a slope inclined at an angle Ѳ to the horizontal of sinѲ=1/50. The wagons move up the slope together against a constant frictional resistance of 50N per tonne. Calculate the distance they travel up the slope before coming to instantaneous rest.
any help would be great
thanks

2. inelastic collision ... momentum is conserved

$m_1v_0 = (m_1 + m_2)v_f
$

let x be the distance both cars travel up the incline and f be the force of friction ... use energy concepts to determine x

kinetic energy after the collision - work done by friction = final gravitational potential energy

$\frac{1}{2}(m_1 + m_2)v_f^2 - f \cdot x = (m_1 + m_2)g \cdot x \sin{\theta}$