Question

A missile of mass 1 kg is moving with speed 10 m/s along the +ve x direction. Its target is a car weighing 100 kg, moving with 1 m/s also in the +ve x direction. The missile hits the target but doesn't burst. Find the combined velocity of car-missile system?

• A. 1 m/s
• B. 10 m/s
• C. $\frac{110}{101}m/s$
• D. $\frac{101}{110}$ m/s

Answer 1

The correct option is C

$\frac{110}{101}m/s$

Take missile & car as a system No external force.

Momentum conserved

$P_i=P_{missile}+P_{car}$

$=1\times 10+100\times 1$

= 110

$P_f=P_{missile+car}$

= (1 + 100) v (assuming car moves with velocity v after missile hits)

$P_f=101v$

Now $\therefore$ No external force so momentum conserved.

$\Delta P=0$

$P_f-P_i=0$

$P_f=P_i$

101 v = 110

$v=\frac{110}{101}m/s$