Answer:
The mass of the first car is 1498.31 kg.
Explanation:
Given that,
Initial speed of an automobile, [tex]u_1=66.9\ km/h = 18.58\ m/s[/tex]
Initial speed of the car is 0 as it is at rest, [tex]u_2=0[/tex]
After the collision, the two cars lock up and they slide together with a speed of, V = 36.1 km/h = 10.02 m/s
The mass of the parked car, [tex]m_2=1280\ kg[/tex]
We need to find the mass of the first car. It is a case of inelastic collision in which two objects stick together. The conservation of momentum follows here. So,
[tex]m_1u_1+m_2u_2=(m_1+m_2)V\\\\m_1u_1=(m_1+m_2)V\\\\m_1u_1=(m_1+m_2)V[/tex]
[tex]m_1[/tex] is the mass of the first car
After rearranging we get :
[tex]m_1=\dfrac{m_2V}{u_1-V}\\\\m_1=\dfrac{1280\times 10.02}{18.58-10.02}\\\\m_1=1498.31\ kg[/tex]
So, the mass of the first car is 1498.31 kg. Hence, this is the required solution.
