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COM in Collision and Explosion

Two balls wit...

Question

Two balls with masses $m_{1}$ = 3 kg and $m_{2}$ = 5 kg have initial velocities $v_{1}$ = 5 m/s = $v_{2}$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM 3 seconds before collision?

-(12 $^i - 15^j$ ) m/s

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(-12 $^i + 15^j$ ) m/s

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(-12 $^i + 15^j$ ) m/s

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(-15 $^i - 12^j$ ) m/s

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Solution

The correct option is B
(-12 $^i + 15^j$ ) m/s

The given time is of no consequence since $V_{C O M}$ is fixed for all times as there is no external force acting on the system of 2 particles.
$V_{c o m})_{x} = \frac{m_{1} (v_{1})_{x} + m_{2} (v_{2})_{x}}{m_{1} + m_{2}} = \frac{(3) (- 5 c o s 37^{\circ}) + 5 (0)}{8} = 15 m / s (V_{c o m})_{x} = \frac{m_{1} (V_{1})_{y} + m_{2} (V_{2})_{y}}{m_{1} + m_{2}} = \frac{3 (- 5 s i n 37^{\circ}) + 5 (5)}{8} = + 2 m / s {\to v}_{c o m} = (- 15^i + 2^J) m / s$

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Two balls with masses m1 = 3 kg and m2 = 5 kg have initial velocities v1 = 5 m/s = v2 in the directions as shown in figure. They collide at the origin. Find the velocity of the COM 3 seconds before collision?

Two balls with masses $m_{1}$ = 3 kg and $m_{2}$ = 5 kg have initial velocities $v_{1}$ = 5 m/s = $v_{2}$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM 3 seconds before collision?