A body of mass m moving with velocity V along the X-axis, collides with another mass M moving with velocity v along the Y-axis. The masses coalesce after collision. Find the velocity and the direction of motion of the combined mass.

Explanation

Let the velocity of the combined mass be u which makes an angle `theta` with the X-axis
Applying the law of conservation of linear momentum along the X-axis,
mV + 0 = (m + M) u cos `theta`
Similarly, along the Y-axis,
0 + Mv = (m + M)u sin`theta`
Squaring and adding (1) and (2)
`m^(2)V^(2) + M^(2)v^(2) = (m + M)^(2) u^(2)`
or, `u^(2) = (m^(2)V^(2)+M^(2)v^(2))/((m + M)^(2))`
Hence, u = `(sqrt(m^(2)V^(2) + M^(2)v^(2)))/(M + m)`
Also, (2) `div` (1) gives,
`tan theta = ("M"v)/(mV)" "or," "theta = tan^(-1) (Mv)/(mV)`.