What Height Must a Jet Begin a Quarter Turn to Avoid Exceeding 5g Acceleration?

[jcumby]

A jet is diving vertically downward at 1200 km/h. If the pilot can withstand a maxiumum acceleration of 5g before losing consciousness, at what height must the plane start a quarter turn to pull out of the dive? Assume the speed remains constant.



I really don't know where to start here...All I've done is convert 1200 km/h to m/s and draw the jet's ideal flight path

 

[tiny-tim]

Welcome to PF!

A jet is diving vertically downward at 1200 km/h. If the pilot can withstand a maxiumum acceleration of 5g before losing consciousness, at what height must the plane start a quarter turn to pull out of the dive? Assume the speed remains constant.

Hi jcumby! Welcome to PF!

Obviously, the jet has to complete the 90º turn before it reaches the ground!

So essentially the question is asking, if you go in a circle at 1200 km/h, what is the radius at which the maximum acceleration is 5g (or is it 4g or 6g ).

 

[minifhncc]

The speed remains constant? So acceleration = 0? Sounds like a dodgy question again...? Maybe someone else can help you.

 

[tiny-tim]

The speed remains constant? So acceleration = 0?

Hi minifhncc!

The speed is constant, but the velocity isn't.

 

[minifhncc]

Well judging by the question, I'd imagine it would've had asked something along the lines of how far it can accelerate down at 9.8ms^-2 and then when or after how much traveling to turn to get the correct force/acceleration for 5g, but anyhow...

 

[tiny-tim]

Well judging by the question, I'd imagine it would've had asked something along the lines of how far it can accelerate down at 9.8ms^-2

Nooo … that would be free-falling … the question is about powered flight, with constant speed.

 

[minifhncc]

Yes, but the question is asking at what height the plane needs to turn so that acceleration is under 5g. It doesn't ask what height it needs to turn to avoid hitting the ground... You see now?

EDIT: I can see where you're getting at, but I still think it's a dodgy question.

 

[tiny-tim]

Yes, but the question is asking at what height the plane needs to turn so that acceleration is under 5g. It doesn't ask what height it needs to turn to avoid hitting the ground... You see now?

EDIT: I can see where you're getting at, but I still think it's a dodgy question.

At constant speed, the acceleration depends only on the radius, not the height!

So why else would the question ask for the height?

Not hitting the ground is very important!​

 

[minifhncc]

Yeah I suck at word based stuff, Maths is my main 'area of expertise' =P

 

[metaender]

An excellent explanation. I was doing the same as OP and completely forgot about circular motion.

Another helpful tip for this question- a = (v²)/r or r = (v²)/a

Don't forget to keep your units uniform.

Hi jcumby! Welcome to PF!

Obviously, the jet has to complete the 90º turn before it reaches the ground!

So essentially the question is asking, if you go in a circle at 1200 km/h, what is the radius at which the maximum acceleration is 5g (or is it 4g or 6g ).