Question

64. Object A of mass 19 kg travels to the east at 4.2 m/s and object B of mass 24 kg travels to the south at 3.6 m/s. They collide and stick together in a perfect inelastic collision as shown below. What is the magnitude and direction (with respect to the horizontal) of the velocity of the two objects after the collision?

Answer 1

Suppose the system of mass

$M(=m_a+m_b)$

after collision moves with speed $V$ in direction $\theta$.

Conservation of momentum in horizontal direction

$m_av_a=MV\cos\theta$

Conservation of momentum in vertical direction

$m_bv_b=MV\sin\theta$

Thus,

$V=\frac{1}{M}\sqrt{m_a^2v_a^2+m_b^2v_b^2}$

and

$\theta=\tan^{-1}\frac{m_bv_b}{m_av_a}$

On inserting the values

V=2.74 m/s

and

$\theta=47.27\degree$