• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • #1
[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.
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6

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.
 
  • #3
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.
 
  • #4
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
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?
 
  • #5
Oh...now I understand this. I would use pythagorean's theorem to get the resultant velocity. Thanks I appreciate your help.
 
  • #6
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
Oh...now I understand this. I would use pythagorean's theorem to get the resultant velocity. Thanks I appreciate your help.
Correct! No problem :smile:
 

Related Threads for: Airplane propeller and plane's velocity relative to the ground.

Replies
1
Views
5K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
5
Views
336
  • Last Post
Replies
2
Views
15K
  • Last Post
Replies
2
Views
577
  • Last Post
Replies
1
Views
6K
Replies
16
Views
4K
Top