Two balls with masses $m_{1} = 3$ kg and $m_{2} = 5$ kg have initial velocities $ν_{1} = ν_{2} = 5 m / s$ in the direction shown in Fig. They collide at the origin.
a. Find the velocity of the $C M$ $3 s$ before the collision.
b. Find the position of the $C M$ $2 s$ after the collision

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Solution

(a) The given time is of no consequences since $ν_{C M}$ fixed for all times.
$= \frac{(3) (- 5 c o s 37^{o}) + (5) (0)}{8 k g} = 1.5 m / s$
$ν_{C M} (y) = \frac{m_{1} ν_{1 y} + m_{2} ν_{2 y}}{m_{1} + m_{2}}$
$= \frac{(3) (- 5 s i n 37^{o}) + (5 \times 5)}{8 k g} = + 2 m / s$
$∴ {\to ν}_{C M} = 1.5^i + 2^j m / s$
(b) Since the collision occurs at the origin $({\to r}_{1} = 0),$ the position of the centre of mass $2 s$ later is ${\to r}_{C M} = {\to r}_{1} + {\to ν}_{C M} t$
${\to ν}_{C M} t = - 3^i + 4^j m$

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Two balls with masses m1=3kg and m2=5kg have initial velocities ν1=ν2=5m/s in the direction shown in Fig. They collide at the origin.a. Find the velocity of the CM 3s before the collision.b. Find the position of the CM 2s after the collision

Two balls with masses $m_{1} = 3$ kg and $m_{2} = 5$ kg have initial velocities $ν_{1} = ν_{2} = 5 m / s$ in the direction shown in Fig. They collide at the origin.
a. Find the velocity of the $C M$ $3 s$ before the collision.
b. Find the position of the $C M$ $2 s$ after the collision