Question

An airplane propeller rotates at 1050 rev/min while the airplane flies at a speed of 510 km/h relative to the ground. The plane's velocity is parallel to the propeller's axis of rotation.

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

Answer 1

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

a) 164.96m/s

b) 217.44m/s

Step-by-step explanation:

The linear speed of a point on the tip of the propeller as seen by the pilot at a radius of 1.5m is given by:

Vp= wr

Where w= angular velocity of the propeller.

r= radius of propeller at the point of interest.

Vp= 1050 ×(2×3.142/60) × 1.5 Vp= 9887.3/60

VP = 164.96m/s

b) The linear velocity of the plane is parallel to the propeller's rotation axis. Then the linear velocity of the plane is perpendicular to the linear velocity of the propeller.

Therefore the linear speed of a point on the tip of the propeller as seen by an observer on the ground st a radius of 1.5m is given by:

Vo= Sqrt(VP + V)^2

Where Vo is linear velocity of plane relative to the ground

Vo= Sqrt(164^2 + [(510×10^3)/(60×60)]^2

Vo= Sqrt(27211.80 + 20069.44)

Vo=Sqrt(47281.25)

Vo= 217.44m/s