Chapter 9, Problem 9.1CYU

Check Your Understanding The U.S. Air Force uses “10gs” (an acceleration equal to $10\times 9.8\text{m}/{\text{s}}^{\text{2}}$ ) as the maximum acceleration a human can withstand (but only tot several seconds) aid survive. How much time must the Enterprise spend accelerating if the humans on board are to experience an average at most 10gs of acceleration? (Assume the inertial dampeners are offline.)

To determine

The time spend by the Enterprise in accelerating.

Answer to Problem 9.1CYU

The time spend by the Enterprise in accelerating is $8.9\text{d}$.

Explanation of Solution

Given:

The acceleration is, $a=10g\text{s}$.

Formula used:

The required time is given by,

$\Delta t=\frac{v_{\text{f}}}{a}$

Here, $\Delta t$ is the required time, $v_{\text{f}}$ is the final speed of the Enterprise and $a$ is the acceleration of the Enterprise.

Calculation:

Since, the final speed of the Enterprise is $v_{\text{f}}=\frac{1}{4}\left(3.0\times {10}^8\text{m}/\text{s}\right)$ then,

The required time iscalculated as,

$\begin{array}{c}\Delta t=\frac{v_{\text{f}}}{a}\\ =\frac{\frac{1}{4}\left(3.0\times {10}^8\text{m}/\text{s}\right)}{10g\text{s}}\\ =\frac{\frac{1}{4}\left(3.0\times {10}^8\text{m}/\text{s}\right)}{\left(10\times 9.8\text{m}/{\text{s}}^2\right)}\\ =7.7\times {10}^5\text{s}\end{array}$

Convert the required time to days as,

$\begin{array}{c}\Delta t=\left(7.7\times {10}^5\text{s}\times \frac{1\text{d}}{86400\text{s}}\right)\\ =8.9\text{d}\end{array}$

Conclusion:

The time spend by Enterprise in accelerating is $8.9\text{d}$.