Airplane propeller and plane's velocity relative to the ground.

[rosstheboss23]

[SOLVED] Airplane propeller and plane's velocity relative to the ground.

Homework Statement

An airplane propeller rotates at 2200 rev/min while the airplane flies at a speed of 550 km/h relative to the ground. The plane's velocity is parallel to the propeller's axis of rotation.
Part a) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by the pilot?

Part b) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by an observer on the ground?

Homework Equations

v=w times r
v=w times r times sin delta

The Attempt at a Solution

I got part a asking speed relative to pilot by converting 2200rev/min to m/s, but part b has me stuck...I don't know if I am missing an equation that I could possibly use but I tried to convert the speed relative to ground to m/s and add it to the 345.57m/s I got as the answer for part a.

 

[Hootenanny]

Homework Statement

An airplane propeller rotates at 2200 rev/min while the airplane flies at a speed of 550 km/h relative to the ground. The plane's velocity is parallel to the propeller's axis of rotation.
Part a) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by the pilot?

Part b) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by an observer on the ground?

Homework Equations

v=w times r
v=w times r times sin delta

The Attempt at a Solution

I got part a asking speed relative to pilot by converting 2200rev/min to m/s, but part b has me stuck...I don't know if I am missing an equation that I could possibly use but I tried to convert the speed relative to ground to m/s and add it to the 345.57m/s I got as the answer for part a.

Notice that the linear velocity of the propeller tip is perpendicular to the velocity of the plane.

 

[rosstheboss23]

Remembering that how would I relate 550km/hr to the speed seen by the pilot that is what has me confused. It should form a 90 degree angle and be the same as I calculated in a, but that doesn't work...I tried v= w times r times sin delta and it didn't work.

 

[Hootenanny]

Remembering that how would I relate 550km/hr to the speed seen by the pilot that is what has me confused. It should form a 90 degree angle and be the same as I calculated in a, but that doesn't work...I tried v= w times r times sin delta and it didn't work.

The speed is the magnitude of the resultant velocity. How do you normally find the magnitude of two perpendicular vectors?

 

[rosstheboss23]

Oh...now I understand this. I would use pythagorean's theorem to get the resultant velocity. Thanks I appreciate your help.

 

[Hootenanny]

Oh...now I understand this. I would use pythagorean's theorem to get the resultant velocity. Thanks I appreciate your help.

Correct! No problem