Question

An airplane requires 20 s and 400 m of runway to become airborne, starting from rest. What is its velocity when it leaves the ground? Please show how to solve.

Answer 1

An airplane requires 20 s and 400 m of runway to become airborne, starting from rest. What is its velocity when it leaves the ground? Please show how to solve.

**Solution.**

$$s = 400\,m, t = 20\,s, v_i = 0;$$ $$v_f - ?$$

A displacement of the airplane, which it moves with acceleration:

$$s = v_i t + \frac{a t^2}{2},$$

$s$ - the displacement of the airplane – runway;

$v_i$ - initial velocity of the airplane;

$a$ - the acceleration of the airplane;

$t$ - time.

$v_i = 0$, because the airplane starting from rest, therefore:

$$s = \frac{a t^2}{2}.$$

A velocity of the airplane, which it moves with acceleration:

$$v_f = v_i + a t,$$

$v_f$ - the final velocity of the airplane.

$$v_f = a t.$$ $$a = \frac{v_f}{t}.$$

We substitute the expression for the acceleration in the equation for the displacement:

$$s = \frac{v_f t^2}{2t} = \frac{v_f t}{2},$$ $$s = \frac{v_f t}{2}.$$

The final velocity of the airplane when it leaves the ground:

$$v_f = \frac{2s}{t}.$$ $$v_f = \frac{2 \cdot 400\,m}{20\,s} = 40\, \frac{m}{s}.$$

Answer: The velocity of the airplane when it leaves the ground is $v_{f} = 40\frac{m}{s}$ .