Answer:
7.40m/s
Explanation:
The masses of the cars with their respective initial velocities are;
[tex] m_1 = 212kg[/tex]
[tex]u_1 = 8.00 m{s}^{ - 1} [/tex]
[tex]m_2 = 196kg[/tex]
[tex]u_1 =6.75m {s}^{ - 1} [/tex]
Since the two car stuck after collision, they all move with a common velocity in the same direction.
Let the velocity at which the two cars will be moving after collision be V.
From the conservation of momentum, in a closed system, momentum before collision is equal to momentum after collision.
Mathematically,
[tex]m_1u_1 +m_2u_2 = (m_1 + m_2)v[/tex]
By substitution, we obtain;
[tex](212 \times 8) +(196 \times 6.75) = (212 + 196)v[/tex]
[tex] \implies1696+1323 =408 \times v[/tex]
[tex] \implies3019 =408 \times v[/tex]
Dividing through by 408, we obtain
[tex] \implies\frac{3019}{408} = \frac{408 \times v }{408} [/tex]
[tex] \implies v =7.3995[/tex]
Therefore,v=7.40m/s
