Q20E - University Physics with Modern Physics

Question

A jet fighter pilot wishes to accelerate from rest at a constant acceleration of to reach Mach 3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will black out if this acceleration lasts for more than5.0s . Use $331m/s$ for the speed of sound. (a) Will the period of acceleration last long enough to cause him to black out? (b) What is the greatest speed he can reach with an acceleration of  before he blacks out?

Step-by-Step Solution

Answer

a) 20.3 is enough time to cause him to blackout, and b) the greatest speed he can reach before he blacks out is$245m/s$ .

Step 1: Identification of the given data

• The acceleration of the jet fighter pilot is 5g .
• The speed of the sound is $331m/s$.

Step 2:Significance of Newton’s first law of the jet

This law describes that a body will continue to move at a uniform speed unless it is resisted by an external force.

The equation of the straight line may be beneficial for identifying the time required for the acceleration and speed of the jet fighter pilot.

Step 3: Determination of the time required and the speed needed for the jet fighter pilot

Here,$v_x$ is the speed of Mach 3 which is and which is$\text{3}\times \left(\text{331m/s}\right)=\text{993m/s}$ the initial speed is 0 m/s. The acceleration of the jet fighter is,and the time taken for the fighter jet is 5s .

a) From Newton’s first law, the equation for the motion of the jet fighter is expressed as:

$$\begin{gathered} v_x=v_{ox}-a_{x}t \\ t=\frac{v_{x-v_{ox}}}{t} \end{gathered}$$

Substituting the values in the above expression, we get-

$\begin{array}{rcl}t & =& \frac{993 m/s-0m/s}{49.0m/s^2}\\ & =& 20.3s\end{array}$

Thus, the time needed which last long enough to cause himto black out is 20.3s.

b) From Newton’s first law, the velocity of the jet fighter is expressed as:

$v_x=v_{0x}+a_{x}t$

Substituting the values in the above expression, we get-

$\begin{array}{rcl}{v}_x& =& 0 m/s+\left(49.0 m/s^2\right)\left(5.0s\right)\\ & =& 245m/s\end{array}$

Thus, the greatest speed he can reach is $=245m/s$