Chapter 11.2, Problem 21PP

To determine

Initial speed of bullet.

Answer to Problem 21PP

11260 cm/s

Explanation of Solution

Given:

Mass of bullet, $m_1=8\text{ g}$

Mass of wooden, $m_2=9\text{ kg}$

Common speed after collision, $v=10\text{ cm/s}$

Formula used:

Momentum of nay object is given by,

  $P=mv$

Here, P is momentum, m is mass and v is velocity.

According to conservation of momentum, if there is no external force applied on the object then momentum is conserved.

  $P_i=P_f$

Calculation:

As the wooden block is at rest.

Therefore, speed of wooden box, $v_1=0\text{ cm/s}$

Now, substituting the value of $m_1,m_2,v_1\text{ and }v$ and solve.

  $m_1{v}_1+m_2{v}_2=\left(m_1+m_2\right)v$

  $\begin{array}{l}9\times 0+0.008v_2=\left(9+0.008\right)\times 10\\ 0.008v_2=90.08\\ v_2=\frac{90.08}{0.008}\\ =11260\text{ cm/s}\end{array}$

Conclusion:

Therefore, initial speed of bullet is 11260 cm/s.