Question

Mass C, which has a mass of 4 kg, is suspended from a cord attached to cart A, which has a mass of 5 kg and can move freely on a frictionless horizontal track. A 6g bullet is fired with a speed $v_0$ = 500 m/s and gets lodged in block C. (Given cos 20 = 0.94)

9. The velocity of C as it reaches its maximum elevation is close to :

• A. 2.51
• B. 0.75
• C. 0.51
• D. 0.31

Answer 1

Answer: (D)

0.31

Answer 2

The system (cart A + block C + bullet) has no external horizontal forces acting on it. Therefore, the total horizontal momentum of this system is conserved.

Initial horizontal momentum = $m_b v_0 \cos 20^\circ$

Final horizontal momentum (at maximum elevation, C and A move with a common horizontal velocity $V_f$) = $(m_A + m_C + m_b) V_f$

$m_b v_0 \cos 20^\circ = (m_A + m_C + m_b) V_f$

$0.006 \, \text{kg} \times 500 \, \text{m/s} \times 0.94 = (5 \, \text{kg} + 4 \, \text{kg} + 0.006 \, \text{kg}) V_f$

$2.82 = 9.006 V_f$

$V_f = \frac{2.82}{9.006} \approx 0.3131 \, \text{m/s}$

The velocity of C as it reaches its maximum elevation is $V_f \approx 0.31 \, \text{m/s}$.