Answer:
A. 14 meters/second to the west
Explanation:
The collision is inelastic, which means that:
- only the total momentum is conserved (not the kinetic energy)
- the two cars stick to each other and continue their motion together after the collision
Therefore, we can write the law of conservation of momentum as follows:
[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2 )v[/tex]
where:
[tex]m_1 = 1.5 \cdot 10^3 kg[/tex] is the mass of the first car
[tex]u_1 = +22 m/s[/tex] is the initial velocity of the first car (let's take as positive the west direction)
[tex]m_2 = 9.0 \cdot 10^2 kg[/tex] is the mass of the second car
[tex]u_2 = 0[/tex] is the initial velocity of the second car
[tex]v[/tex] is the final velocity of the two cars
Re-arranging the equation, we get:
[tex]v=\frac{m_1 u_1}{m_1 +m_2}=\frac{(1.5\cdot 10^3 kg)(+22 m/s)}{1.5\cdot 10^3 kg+9.0\cdot 10^2 kg}=+13.8 m/s[/tex]
So, approximately 14 m/s, and the direction is still west since the sign is positive.
