Final answer:
To determine the fraction of engine power used for climbing, calculate the power used for climbing and compare it to the total engine power.
Step-by-step explanation:
To determine the fraction of engine power used to make the airplane climb, we need to calculate the power used for climbing and compare it to the total engine power. The power used for climbing is equal to the work done to gain gravitational potential energy divided by the time taken:
Power for climbing = Work done / Time taken
The work done to gain gravitational potential energy is given by the formula:
Work = Force * Distance
We can find the force by multiplying the mass of the airplane by the acceleration due to gravity, and the distance by multiplying the average speed of the airplane by the time taken to climb:
Force = mass * gravity
Distance = speed * time
Finally, we can substitute the values and calculate the power for climbing. To find the fraction, we divide the power for climbing by the total engine power.