Answer
The velocity after the collision is $~2.06~m/s$
Work Step by Step
By conservation of momentum, the final momentum of the system is equal to the initial momentum.
We can find the east component $p_x$ of the momentum:
$p_x = (2.00~kg)(2.70~m/s) = 5.40~kg~m/s$
We can find the south component $p_y$ of the momentum:
$p_y = (1.50~kg)(3.20~m/s) = 4.80~kg~m/s$
We can find the magnitude of the momentum:
$p = \sqrt{p_x^2+p_y^2} = \sqrt{(5.40~kg~m/s)^2+(4.80~kg~m/s)^2} = 7.225~kg~m/s$
We can find the final velocity $v_f$ after the collision:
$m_f~v_f = p$
$v_f = \frac{p}{m_f}$
$v_f = \frac{7.225~kg~m/s}{2.00~kg+1.50~kg}$
$v_f = 2.06~m/s$
The velocity after the collision is $~2.06~m/s$.
