Answer to Question #236327 in Physics for eshiii

Question

4. An airplane requires a speed of 80 mi/hr to be airborne. It start from rest on a runway 1600 ft long. a) What must be the minimum safe acceleration of the airplane? b) With this acceleration, how many seconds will it take for the plane to acquire its needed speed for take off? 

Answer 1

(a)

$$v^2=v_0^2+2as,$$ $$a=\dfrac{v^2}{2s},$$ $$a=\dfrac{(80\ \dfrac{mi}{hr}\cdot\dfrac{1609\ m}{1\ mi}\cdot\dfrac{1\ hr}{3600\ s})^2}{2\cdot1600\ ft\cdot\dfrac{0.3048\ m}{1\ ft}}=1.31\ \dfrac{m}{s^2}.$$

(b)

$$v=v_0+at,$$ $$t=\dfrac{v}{a}=\dfrac{80\ \dfrac{mi}{hr}\cdot\dfrac{1609\ m}{1\ mi}\cdot\dfrac{1\ hr}{3600\ s}}{1.31\ \dfrac{m}{s^2}}=27.3\ s.$$