Question

The propeller of a World War II fighter plane is 2.30 m in diameter. What is the linear speed of the tip of the propeller when the plane is flying at a constant speed?

a) 86.9 m/s
b) 97.5 m/s
c) 105.2 m/s
d) 114.7 m/s

Answer 1

The linear speed of the tip of the propeller is approximately 144.51 m/s.

Step-by-step explanation:

The linear speed of the tip of the propeller can be calculated using the formula:

v = r●ω

Where v is the linear speed, r is the radius of the propeller, and ●ω is the angular speed of the propeller.

Given that the diameter of the propeller is 2.30 m, the radius can be calculated by dividing the diameter by 2: r = 2.30 / 2 = 1.15 m.

The angular speed is given by the rotation rate of the propeller, so we need to convert the rotation rate from rev/s to rad/s. 1 rev = 2π rad, so ω = 20 rev/s × 2π rad/rev = 40π rad/s.

Now we can substitute the values into the formula: v = 1.15 m × 40π rad/s = 46π m/s ≈ 144.51 m/s.

Therefore, the linear speed of the tip of the propeller is approximately 144.51 m/s.