Question

A pilot who accelerates at more than 4 g begins to "gray out" but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 m/s for the speed of sound in cold air.)

Answer 1

Answer:

33.7410805301 s

22336.5953109 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity = $4\times 331$

s = Displacement

a = Acceleration = $4g=4\times 9.81\ m/s^2$

g = Acceleration due to gravity = 9.81 m/s²

$v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{4\times 331-0}{4\times 9.81}\\\Rightarrow t=33.7410805301\ s$

The time taken is 33.7410805301 s

$s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 4\times 9.81\times 33.7410805301^2\\\Rightarrow s=22336.5953109\ m$

The plane would travel 22336.5953109 m