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A jet fighter pilot wishes to accelerate from rest at a constant acceleration of 5 g 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 than 5.0 s. Use 331 m/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 5g before he blacks out?

Answer :

boffeemadrid

Answer:

20.244648318 s

10051.4678899 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity = [tex]3\times 331[/tex]

s = Displacement

a = Acceleration = [tex]5g=5\times 9.81\ m/s^2[/tex]

g = Acceleration due to gravity = 9.81 m/s²

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{3\times 331-0}{5\times 9.81}\\\Rightarrow t=20.244648318\ s[/tex]

The time taken is 20.244648318 s

[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 5\times 9.81\times 20.244648318^2\\\Rightarrow s=10051.4678899\ m[/tex]

The plane would travel 10051.4678899 m

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