Answer:
V = 29.49 m/s
Explanation:
Given that,
The mass of a car,[tex]m_c=2100\ kg[/tex]
The mass of a motorcycle, [tex]m_m=290\ kg[/tex]
The initial velocity of the car,[tex]v_c=30i-10j[/tex]
[tex]|v_c|=\sqrt{30^2+(-10)^2} =31.62\ m/s[/tex]
The initial velocity of the motorcycle,[tex]v_m=10i+10j[/tex]
[tex]|v_m|=\sqrt{10^2+10^2} =14.14\ m/s[/tex]
As they stick together. Let V is the speed. So, using the conservation of momentum,
[tex]m_cv_c+m_mv_m=(m_c+m_m)V\\\\V=\dfrac{m_cv_c+m_mv_m}{(m_c+m_m)}\\\\V=\dfrac{2100\times 31.62+290\times 14.14}{(2100+290)}\\\\V=29.49\ m/s[/tex]
So, the velocity of the stuck together car and the motorcycle after the collision is 29.49 m/s.
