The car and the truck move together at 6.16 m/s after the collision.
Explanation:
The problem can be solved by using the principle of conservation of momentum. In fact, in absence of external forces, the total momentum of the system must be conserved before and after the collision.
Therefore, we can write:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]
where:
[tex]m_1 = 1250 kg[/tex] is the mass of the first car
[tex]u_1 = 0[/tex] is the initial velocity of the first car (it was at rest)
[tex]m_2 = 3550 kg[/tex] is the mass of the truck
[tex]u_2 = 8.33[/tex] is the initial velocity of the truck
[tex]v[/tex] is the final velocity at which the car and the truck move together after the collision
Therefore, we can re-arrange the equation and solve for v, the final velocity of the two vehicles:
[tex]v = \frac{m_2 u_2}{m_1+m_2}=\frac{(3550)(8.33)}{1250+3550}=6.16 m/s[/tex]
So, the car and the truck move together at 6.16 m/s.
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