Final answer:
To find the time it would take for the airplane to reach a speed of 250 m/s and an altitude of 12.0 km, we use the equations of motion. First, we find the time for the speed of 250 m/s, which is approximately 0.375 seconds. Then, we find the time for the altitude of 12.0 km, which is approximately 6 seconds.
Step-by-step explanation:
To find the time it would take for the airplane to reach a speed of 250 m/s and an altitude of 12.0 km, we need to use the equations of motion.
First, let's find the time it takes for the airplane to reach the speed of 250 m/s. We can use the equation:
v = u + at
Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Given that the initial velocity is 0 m/s, the final velocity is 250 m/s, and the acceleration is unknown, we can rearrange the equation to solve for time:
t = (v - u) / a
Since the acceleration is constant, we can use the formula:
a = P / m
Where P is the power and m is the mass.
Given that the power is 100 MW and the mass is 1.50 x 10^5 kg, we can substitute these values into the equation:
a = 100 MW / (1.50 x 10^5 kg)
Be sure to convert the power from MW to W by multiplying it by 10^6, so the equation becomes:
a = (100 x 10^6 W) / (1.50 x 10^5 kg)
Simplify the equation to find the acceleration:
a = 666.67 m/s^2
Now substitute the values of velocity and acceleration into the equation:
t = (250 m/s - 0 m/s) / 666.67 m/s^2
Solve for time:
t = 0.375 s
Therefore, it would take approximately 0.375 seconds for the airplane to reach a speed of 250 m/s.
To find the time it takes for the airplane to reach an altitude of 12.0 km, we need to use the equation:
s = ut + (1/2)at^2
Where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time taken.
Given that the acceleration is the same as before (666.67 m/s^2), the initial velocity is 0 m/s, and the displacement is 12.0 km (which is equal to 12000 m), we can rearrange the equation to solve for time:
t = sqrt((2s) / a)
Substitute the values into the equation:
t = sqrt((2 x 12000 m) / 666.67 m/s^2)
Calculate the square root and simplify the equation:
t = sqrt(36)
t = 6 s
Therefore, it would take approximately 6 seconds for the airplane to reach an altitude of 12.0 km.