A pilot who accelerates at more than 4g begins to 'gray out' but doesn't completely lose consciousness. (b) How far would the plane travel during this period of acceleration? (Use 331 m/s for the speed of sound in cold air.)

Video transcript

Welcome back everybody. We are told that we are trying to get an aircraft to a speed of Mach 10, we're told that it's going to have a constant acceleration of five Gs and we want to figure out the distance traveled in this period of acceleration before we even jump into the problem here, let's simplify these terms a little bit. So Mach 10 is simply calculated by multiplying the speed of sound by whatever this number is. So in this case times 10 we're told that we're gonna use the speed of sound in cold air to be 331 m per second. So that multiplied by 10 will be m per second. Now five Gs of acceleration is just five times the acceleration due to gravity. So this is going to be five times 9.81, which is equal to 49 point oh five m per second squared. Now this Mach 10 here, that is just a velocity that we wish to be our final velocity of velocity we wish to achieve. And since we have a velocity and acceleration and trying to find a displacement. All signs point to us using our chromatic formulas. So we're gonna go ahead and use this one. Our final velocity squared is equal to our initial velocity plus two times our acceleration times our displacement. Now we have a lot of these terms. So let's just go ahead and plug them in. Final velocity we said is 3310 m per second square that is the speed we're trying to achieve. This is going to be equal to our initial velocity. Well, for any aircraft, it's going to start off from nothing. So zero squared plus two times are five Gs of constant acceleration, 49.05 times our displacement acts. So if you divide by this term on both sides, we get that are dealt to access somewhere in the range of 100 and 11,000 m. But to make it simpler, it is 100 and 11.7 kilometers, which corresponds to our answer of thank you guys for watching. Hope this video helped and we will see you all in the next one.