Question

(a) How long would it take a 1.50×105-kg airplane with engines that produce 100 MW of power to reach a speed of 250 m/s and an altitude of 12.0 km if air resistance were negligible?

(b) If it actually takes 900 s, what is the power?
(c) Given this power, what is the average force of air resistance if the airplane takes 1200 s? (Hint: You must find the distance the plane travels in 1200 s assuming constant acceleration.)

Answer 1

To answer part (a), we can use the equations of motion to determine the time it takes for the airplane to reach the desired speed and altitude. For part (b), we can rearrange the power equation to solve for power. Finally, for part (c), we need to find the distance the airplane travels in 1200 s assuming constant acceleration.

Step-by-step explanation:

To answer part (a), we can use the equations of motion to determine the time it takes for the airplane to reach the desired speed and altitude. First, we need to convert the power from megawatts (MW) to watts (W) by multiplying by 10^6. Then, we can use the equation:

Power (P) = force (F) × velocity (v)

Since we know the power and the mass of the airplane, we can rearrange the equation to solve for force:

Force = Power / velocity

Next, we can use the equation:

Force = mass (m) × acceleration (a)

Since we want to find the time it takes for the airplane to reach the desired speed and altitude, we need to find the acceleration. The distance traveled (d) can be calculated using the equation:

d = 0.5 × acceleration × time^2

By rearranging the equation, we can solve for acceleration:

acceleration = 2d / time^2

Now, we have all the necessary information to solve for time:

time = velocity / acceleration

Substituting the given values into the equation will give us the time it takes for the airplane to reach the desired speed and altitude. For part (b), we can rearrange the power equation to solve for power:

Power = Force × velocity

By substituting the given values into the equation, we can determine the power. Finally, for part (c), we need to find the distance the airplane travels in 1200 s assuming constant acceleration. We can use the equation:

d = 0.5 × acceleration × time^2

By rearranging the equation, we can solve for acceleration:

acceleration = 2d / time^2

Once we have the acceleration, we can calculate the average force of air resistance using the equation:

Force = mass × acceleration

By substituting the given values into the equation, we can find the average force of air resistance.