Question

3 Engine RBO

Target Gross Weight: ____
Vmca: ____
Final Flap Setting: ____
Fuel Flow Settings: ____
Vref: ____
Approach Speed: ____
Actions at 500 ft: ____
Actions at 300 ft: ____
Power Idle at: ____

Answer 1

The student's question pertains to the physics of a detached aircraft propeller, focusing on its translational velocity and constant rotation rate upon hitting the ground. The translational velocity is determined by the time it takes to fall 300 meters under gravity, while the rotation rate remains unchanged due to conservation of angular momentum.

Step-by-step explanation:

The question involves applying concepts of physics to an aircraft scenario where there is an unexpected loss of a propeller. Specifically, it asks about the translational velocity at which the propeller will hit the ground and its rotation rate afterwards, neglecting air resistance.

Given that the propeller detaches at a height of 300 meters and an initial horizontal velocity of 40.0 m/s, we can use kinematic equations to find the time it takes for the propeller to hit the ground. The vertical motion is independent of the horizontal motion, so we only need to consider the initial vertical velocity (which is 0 m/s as it falls straight down), acceleration due to gravity (9.81 m/s2), and the distance it falls.

The rotation rate of the propeller after it detaches is initially 20 rev/s, and since no external torques are mentioned, we can assume that it will remain constant as it falls (conservation of angular momentum). Therefore:

1. The translational velocity of the propeller as it hits the ground is calculated by using the formula ∙f = ∙o + at, where ∙f is the final velocity, ∙o is the initial velocity (0 m/s), a is the acceleration due to gravity, and t is the time it takes to fall the 300 meters.
2. The rotation rate of the propeller remains at 20 rev/s.

For part (a), to find the time 't', we can use the kinematic equation: distance = ∙ot + ½ at2, and solve for 't'. After finding 't', we can plug it back into the first equation to find the final velocity, ∙f. For part (b), as mentioned, the rotation rate of the propeller does not change due to the conservation of angular momentum, assuming no other external torques act on the propeller after detachment.