Question

An engineer must design a runway to accommodate airplanes that must reach a ground velocity of 61 m/s before they can take off. These planes are capable of being accelerated uniformly at the rate of 2.5 m/s(2). How long will it take the planes to reach takeoff speed? What must be the minimum length of the runway?

Answer 1

An engineer must design a runway to accommodate airplanes that must reach a ground velocity of $61\ \mathrm{m/s}$ before they can take off. These planes are capable of being accelerated uniformly at the rate of $2.5\ \mathrm{m/s}(2)$. How long will it take the planes to reach take off speed? What must be the minimum length of the runway?

Velocity of the airplane equals:

$$v = a t$$

where $a$ – acceleration, $t$ – time.

Therefore, time equals:

$$t = \frac {v}{a} = \frac {61}{2.5} \ s = 24.4 \ s$$

During this time plane covers the distance:

$$d = \frac {a t ^ {2}}{2} = \frac {2.5 (24.4) ^ {2}}{2} \ m = 744 \ m$$

Answer: time equals $24.4\ s$, minimum length of the runway equals $744\ m$