Question

A 300-kg truck moving rightward with a speed of 5 km/hr collides head on with a 1000kg car moving leftward with a speed of 100 km/hr. The two vehicles stick together and move with the same velocity after the collision determine the post - collision speed of the car and truck

Answer 1

Answer:

The final velocity of the vehicles will be -75km per hour (leftwards).

Explanation:

Let us call $m_1$, $v_1$ mass and velocity of the truck , $m_2, v_2$ mass and velocity of the car, and $v_f$ the final velocity of the vehicles.

The law of conservation of momentum states that

$m_1v_1-m_2v_2= v_f(m_1+m_2)$

solving for $v_f$ we get:

$v_f = \dfrac{m_1v_1-m_2v_2}{m_1+m_2}$

putting in numerical values

$m_1 =300 kg \\v_1 =5km/hr = 1.39m/s\\m_2 = 1000kg\\v_2 = 100km/hr = 27.78m/s$

$v_f = \dfrac{300*(1.39)-1000*(27.78)}{300+1000}$

$\boxed{v_f = -21.0m/s }$ (the negative sign indicates that the vehicles are moving in the leftward direction)

or -75.8 km per hour.