Accelerate to the Skies: The Joy of Takeoff

How fast must an airplane reach for takeoff?

An airplane must reach a velocity of 71 m/s for takeoff. If the runway is 1.0 km long, what must the constant acceleration be?

Takeoff Thrills Await!

The constant acceleration required for the airplane to take off is approximately 2.5205 [tex]m/s^{2}[/tex].

Takeoff is a thrilling moment as the airplane accelerates to break free from the constraints of gravity. To achieve this exhilarating feat, the airplane must reach a velocity of 71 m/s before it can soar into the skies. But how does it manage to achieve this speed in such a short distance?

The key lies in the concept of acceleration, the rate of change of velocity with respect to time. In the case of our airplane, it needs a constant acceleration to reach the required takeoff velocity within the given runway length.

Using the kinematic equation [tex]v^2 = u^2 + 2a * s[/tex], where: - v = final velocity (71 m/s) - u = initial velocity (0 m/s, as the airplane starts from rest) - a = constant acceleration (unknown) - s = displacement (runway length = 1.0 km = 1000 meters)

By plugging in the values and simplifying the equation, we find that the constant acceleration required for the airplane to take off is approximately 2.5205 [tex]m/s^{2}[/tex]. This acceleration propels the airplane down the runway with enough force to achieve the desired velocity for liftoff.

So, next time you witness the sheer joy of an airplane gracefully ascending into the sky, remember the magic of acceleration that makes it all possible. Accelerate to the skies and embrace the wonder of flight!