Question

A 30 kg projectile moving horizontally with a velocity ${\overrightarrow{v}}_0=\left(120m/s\right)\hat{i}$ 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.

• A. (360, -45, 32)
• B. (400, -91, 32)
• C. (400, -91, 48)
• D. (360, -91, 48)

Answer 1

The correct option is B (400, -91, 32)

Initial coordinates of CM = (0, 0, 0)
x coordinates of CM after 3 s,
$x_{CM}=120\times 3=360m$
y coordinates of CM after 3 s,
$y_{CM}=-\frac{1}{2}g{t}^2=-45m$
After 3 s,
$(m_1+m_2)x_{CM}=m_1{x}_1+m_2{x}_2$
$x_2=\frac{30\times 360-12\times 300}{18}=400m$
Similarly, $(m_1+m_2)y_{CM}=m_1{y}_1+m_2{y}_2$
$-30\times 45=12\times 24+18\times y_2$
$y_2=-91m$
and in z coordinate, $m_1{z}_1+m_2{z}_2=0\Rightarrow z_2=32m$