A 30 kg projectile moving horizontally with a velocity →v0=(120m/s)^i &#x

Question

A 30 kg projectile moving horizontally with a velocity

{\to v}_{0} = (120 m / s)^i

explodes into two fragments A and B of masses 12 kg and 18 kg, respectively. Taking point of explosion as origin and knowing that 3 s later the position of fragment A is (300, 24, –48) m, determine the position of fragment B at the same instant.

Options:

A . (360, -45, 32)

B . (400, -91, 32)

C . (400, -91, 48)

D . (360, -91, 48)

Answer: Option B
:
B
Initial coordinates of CM = (0, 0, 0)
x coordinates of CM after 3 s,

x_{C M} = 120 \times 3 = 360 m

y coordinates of CM after 3 s,

y_{C M} = - \frac{1}{2} g t^{2} = - 45 m

After 3 s,

(m_{1} + m_{2}) x_{C M} = m_{1} x_{1} + m_{2} x_{2}

x_{2} = \frac{30 \times 360 - 12 \times 300}{18} = 400 m

Similarly,

(m_{1} + m_{2}) y_{C M} = m_{1} y_{1} + m_{2} y_{2}

- 30 \times 45 = 12 \times 24 + 18 \times y_{2}

y_{2} = - 91 m

and in z coordinate,

m_{1} z_{1} + m_{2} z_{2} = 0 \Rightarrow z_{2} = 32 m

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