Chapter 7, Problem 14P

To determine

To Find: The amount of mass must be expelled.

Explanation of Solution

Given:

Total mass of the rocket, $m_R=3180\text{kg}$

Initial velocity of the rocket, $u_R=115.0\text{m/s}$

Speed of gases that are expelled by the rocket, $v_g=1750\text{m/s}$

The course should be altered by $35.0°$ .

The rockets can be fired in perpendicular direction.

Formula Used:

As per law of conservation of momentum,

  $p_i=p_f$

Here, $p_i$ is the initial momentum and $p_f$ is the final momentum.

Calculations:

In the perpendicular direction, apply the law of conservation of momentum. Let the mass of the expelled gases be $m_g$ . To change the direction, additional velocity needs to be added.

  $v_a=v_R\tan \theta$

  

  $\begin{array}{l}{p}_i=p_f\\ 0=m_g{v}_g+\left(m_R-m_g\right)v_a\\ m_g=\frac{m_R{v}_a}{v_a-v_g}\\ m_g=\frac{3180\times 115\tan 35.0°}{115\tan 35.0°-\left(-1750\right)}\\ m_g=140\text{kg}\end{array}$

Conclusion: 

Thus, the amount of expelled massmust be $140\text{kg}$ .