The greatest speed pilot can reach with an acceleration of 5g before he blacks out is 240 m/s.
The acceleration due to gravity is g.
g = 9.8 m/s²
The acceleration of the jet is,
[tex]Acceleration = Mass \times Gravity[/tex]
[tex]a = m \times g[/tex]
[tex]a = 5 \times 9.8[/tex]
[tex]a = 49 \: m/s ^{2} [/tex]
The acceleration of the jet is 49 m/s².
Let the speed of sound be v.
[tex]v = 331 \: m/s[/tex]
Let the initial velocity of the jet be
[tex]Let \: the \: initial \: velocity \: of \: the \: jet \: [/tex]
[tex]be \: v _i.[/tex]
[tex]v _i = 0[/tex]
The time at which the pilot will black out with 49 m/s² acceleration = 4.9 s
Let the time taken to reach Mach 3 be t.
Then the final velocity will be,
[tex]v _f = 3 \times v[/tex]
[tex]v _f = 3 \times 331[/tex]
[tex]v _f = 993 \: m/s[/tex]
[tex]v _f = v _i + at[/tex]
[tex]993 = 0 + (49)t[/tex]
[tex]t = 20.26 \: s[/tex]
Thus, the time taken to reach Mach 3 is 20.26 s.it is greater than the time interval at which the pilot will black out. So the pilot will black out.
The greatest speed pilot can reach with an acceleration of 5g before he blacks out is,
[tex]v _f = 0 +( 49 \times 4.9)[/tex]
[tex]v _f = 240.1 \: m/s[/tex]
Therefore, the greatest speed pilot can reach with an acceleration of 5g before he blacks out is 240 m/s.
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