Question

A 3520 kg truck moving north makes an INELASTIC collision with an 1480 kg car moving 13.0 m/s east. After colliding, they have a velocity of 9.80 m/s at 66.9 degrees. What was the initial velocity of the truck? (m/s)

Answer 1

Answer:

v = 12.8 m/s

Explanation:

• Assuming no external forces acting during the collision, total momentum must be conserved.
• Since momentum is a vector, their components must be conserved too.
• Choosing a pair of axes coincident with the N-S and W-E directions, naming x to the W-E axis and y to the N-S one, we can write the following algebraic equations:      

       $p_{ox} = p_{fx} (1)$

       $p_{oy} = p_{fy} (2)$

• Since we know all the information needed to solve (1), assuming a completely inelastic collision, we can focus in (2), writing both sides of the equation as follows:

       $p_{oy} = m_{t} * v_{ot} = 3520 kg* v_{ot} (3)$

       $p_{fy} = m_{f} * v_{fy} = 5000 kg* 9.8 m/s * sin 66.9 = 45080 kg*m/s (4)$

• Since (4) and  (3) are equal each other, we can solve for vot, as follows:

       $v_{ot} =\frac{45080kg*m/s}{3520kg} = 12.8 m/s (5)$