Answer:
a). 7594 kg m/s^2
Explanation:
The initial momentum of the cars before the collision is the sum of the individual momenta
The momentum of the first car is
[tex]p_1=m_1v_1=78\operatorname{kg}\cdot60m/s=4680\operatorname{kg}m/s[/tex]
The momentum of the second car is
[tex]p_2=m_2v_2=62\operatorname{kg}\cdot47m/s=2914\operatorname{kg}\cdot m/s[/tex]
Hence, the total momentum is
[tex]p_{\text{tot}}=p_1+p_2=4680+2914=\boxed{7594\operatorname{kg}\cdot m/s}[/tex]
which is our answer!
When the cars collide, the conservation of momentum gives
[tex]p_1+p_2=(m_1+m_2)v_f[/tex]
where vf is the final velocity of the stuck-together cars.
solving for vf gives
[tex]v_f=\frac{p_1+p_2}{m_1+m_2}[/tex]
since p1 + p2 = 7594 and m1 = 78 kg and m2 = 62kg; therefore,
[tex]v_f=\frac{7594}{62+78}[/tex][tex]\boxed{v_f=54.24m/s}[/tex]
part (ii).
A sketch of the situation is given below.
