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Question

A hobbyist owns an ultralight airplane that requires a speed of 16 m/s in order to take
off. Starting from a dead stop, the airplane engine can provide 3.2 m/s2
of average acceleration.
The hobbyist has a 50 meter (150-foot) wide back yard, with no fences around it. Will he
be able to take off from his back yard?

Answer 1

The plane needs to get from 0 m/s to 16 m/s at a constant acceleration of 3.2 m/s².  Solve this using the kinematic equation

 

v_f² - v_i² = 2ad

 

v_f = final speed = 16 m/s

v_i = initial speed = 0 m/s

a = constant acceleration = 3.2 m/s²

d = distance over which the acceleration occurs

 

Solve for d.  If d ≤ 50 m, the plane can take off.

 

d = (v_f² - v_i²)/(2a) = (16² - 0²)/[2(3.2)] m = 40 m

 

d = 40 m < 50 m, so there is enough runway for takeoff.