Explanation:
Mass of the car, m = 1500 kg
Initial speed of the car, u = 25 m/s east
Mass of the van, m' = 2500 kg
Initial speed of van, u' = 20 m/s north
It is assumed that the vehicles undergo a perfectly inelastic collision. The law of conservation of linear momentum gives the velocity after the collision as :
[tex]mu+m'u'=(m+m')V\\\\V=\dfrac{mu+m'u'}{(m+m')}\\\\V=\dfrac{1500\times 25i+2500\times 20j}{(1500+2500)}\\\\V=\dfrac{37500i+50000j}{4000}\\\\V=\dfrac{37500i}{4000}+\dfrac{50000j}{4000}\\\\V=(9.37i+12.5j)\ m/s[/tex]
Magnitude of velocity,
[tex]|V|=\sqrt{9.37^2+12.5^2} =15.62\ m/s[/tex]
Direction,
[tex]\tan\theta=\dfrac{12.5}{9.37}=53.14^{\circ}[/tex]
