Chapter 9, Problem 56A

To determine

The time for which a rocket should be fired to have the speed change of $63\text{cm/s}$ .

Answer to Problem 56A

  $1296\text{s}$

Explanation of Solution

Given:

The mass of the spacecraft, $m=72,000\text{kg}$

Thrust on the spacecraft by the rocket, $F=35\text{N}$

Speed change of the spacecraft, $\Delta v=63\text{cm/s = 0}.63\text{m/s}$

Formula used:

Momentum of an object of mass m and moving with velocity v is given by,

  $p=mv$

Impulse on an object is equal to the change in momentum of an object,

  $\text{Impulse = }F\Delta t=p_f-p_i$

Where $F$ is the applied force for time $\Delta t$ , $p_f$ is the final momentum, $p_i$ is the initial momentum.

Calculation:

Using all the given values in the formula mentioned above, the time for which a rocket should be fired, or the time for which the force should be applied by the rocket on the spacecraft, will be,

  $\begin{array}{c}F\Delta t=m\left(v_f-v_i\right)\\ \left(35\right)\Delta t=72000\left(0.63\right)\\ \Delta t=1296\text{s}\end{array}$

Conclusion:

Thus, the time for which a rocket should be fired is $1296\text{s}$ .