Answer:
8.33 m/s, 36.87° North of East
Explanation:
[tex]m_n[/tex] = Mass of car = 1000 kg
[tex]v_n[/tex] = Velocity of car = 15 m/s
[tex]m_e[/tex] = Mass of truck = 2000 kg
[tex]v_e[/tex] = Velocity of truck = 10 m/s
M = Combined mass = 1000+2000 = 3000 kg
Momentum
[tex]p_n=m_nv_n\\\Rightarrow p_n=1000\times 15\\\Rightarrow p_n=15000\ kgm/s[/tex]
Momentum of car traveling East is 15000 kgm/s
[tex]p_e=m_ev_e\\\Rightarrow p_n=2000\times 10\\\Rightarrow p_n=20000\ kgm/s[/tex]
Momentum of truck traveling North is 20000 kgm/s
Angle
[tex]\theta=tan^{-1}\frac{p_n}{p_e}\\\Rightarrow \theta=tan^{-1}\frac{15000}{20000}\\\Rightarrow \theta=36.87^{\circ}[/tex]
As the two vehicles are vectors, the resultant velocity is
[tex](Mv)^2=p_n^2+p_e^2\\\Rightarrow v=\sqrt{\frac{p_n^2+p_e^2}{M^2}}\\\Rightarrow v=\sqrt{\frac{15000^2+20000^2}{3000^2}}\\\Rightarrow v=8.33\ m/s[/tex]
Velocity of the two vehicles when they are locked together is 8.33 m/s and direction is 36.87° North of East
