Question

In the given figure, a 3.50 g bullet is fired horizontally at two blocks at rest on a frictionless table.The bullet passes through block 1 (mass 1.20 kg) and embeds itself in block 2 (mass 1.80 kg). The blocks end up with speeds $v_1=0.630m/s$ and $v_2=1.40m/s$ (Fig b). Neglecting the material removed from block 1 by the bullet, then

• A. the speed of the bullet as it leaves the block 1 is 720 m/s
• B. the speed of the bullet as it leaves the block 1 is 360 m/s
• C. the speed of the bullet as it enters the block 1 is 936 m/s
• D. the speed of the bullet as it enters the block 1 is 1355 m/s

Answer 1

Answer: (A), (C)

the speed of the bullet as it enters the block 1 is 936 m/s

Given that
mass of bullet $\left(m_1\right)3.50g=0.0035kg$
mass of block 1 $\left(m_1\right)=1.20kg$
mass of block 2 $\left(m_2\right)=1.80kg$
$v_1=0.630m/s$
$v_2=1.40m/s$
Applying momentum conservation just before the bullet strikes the second block to the situation where the bullet is embedded within the block.
$\Rightarrow \left(0.0035kg\right)v=\left(1.8kg\right)\times \left(1.4m/s\right)$
$\Rightarrow v=\frac{1.8\times 1.4}{0.0035}$
$\Rightarrow v=720m/s$
Again apply momentum conservation to relate the situation just before the bullet strikes the first block to the instant it has passed through it .
$\Rightarrow \left(0.0035kg\right)v_0=\left(1.2kg\right)\left(0.630m/s\right)+(0.0035kg\times 720m/s)$
$\Rightarrow v_0=936m/s$
Hence, option a and c are correct