What Is the Velocity Change of a Fighter Plane in Horizontal Circular Motion?

[nesan]

Homework Statement

a fighter plane is moving in a horizontal circular path at a constant speed, it takes 9.8 seconds to change its heading by one quarter of a circle from north to east, if the radius of the curvature is 2.0 x 10^3, find

d) the velocity change

The Attempt at a Solution

v = d / t

d = square root ((2.0 x 10^3)^2 + (2.0 x 10^3)^2)

d ≈ 2828m

d / t = 288.6m/s

But the textbook says the answer is 4.5 x 10^2 m/s

I have no idea, in what other ways I can approach this. Help please. :( Pointing me in the right direction will do. ^_^ Thank you.

 

[gneill]

The plane didn't take a straight line from the starting position to the final position over the 9.8 seconds.

Instead, why not think first of the angular velocity, since the plane is describing a circle and you're essentially given the angle it goes through over the 9.8 seconds. If you have the angular velocity and the radius, what is the corresponding tangential speed?

After that, what are the two vectors that represent the starting velocity and final velocity? What's the change between them?

 

[nesan]

The plane didn't take a straight line from the starting position to the final position over the 9.8 seconds.

Instead, why not think first of the angular velocity, since the plane is describing a circle and you're essentially given the angle it goes through over the 9.8 seconds. If you have the angular velocity and the radius, what is the corresponding tangential speed?

After that, what are the two vectors that represent the starting velocity and final velocity? What's the change between them?

Can you explain a bit more on what you mean by angular velocity please? Thank you. :)

EDIT : We haven't learned about tangential velocity and such, could you please explain it in-terms of a beginner, please and thank you. :)

NVM got it.

distance / time = speed

square root (speed ^2 + speed ^2) = average velocity

:)

Thank you. :)

 

[azizlwl]

How do you measure a distance if you're travel in a circle?
This must involve the arc distance along the circle.

Since the aircraft in flying in a circle, the angular speed is used.
But there's relation between angular and linear motion.
One of them velocity, ωr=v, where ω is angular speed dθ/dt(radian per second)

When you got the velocity at 2 points use vector subtraction to find the difference/change.