Question

A certain aircraft has a liftoff speed of 116 km/h.(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 276 m?_____ m/s2(b) How long does it take the aircraft to become airborne?_____ s

Answer 1

(a) 1.88 m/s²

(b) 17.14 s

Explanation:

Given:

Distance (d) = 276 m

Initial speed (u) = 0 m/s

Final speed (v) = 116 km/h

We convert from km/h to m/s, as follows:

`116(km)/(h)\cdot\frac{1000\text{ m}}{1\text{ km}}\cdot\frac{1\text{ h}}{3600\text{ s}}=32.22\text{ m/s}`

(a)

We calculate the acceleration as follows:

`\begin{gathered} v^2=u^2+2ad \\ \\ \text{ we replacing:} \\ \\ (32.22)^2=0^2+2\cdot a\cdot276 \\ \\ a=(32.22^2)/(2\cdot276) \\ \\ a=1.88\text{ m/s}^2 \end{gathered}`

(b)

Finally, we calculate the time, just like this:

`\begin{gathered} v=u+at \\ \\ \text{ we replacing:} \\ \\ 32.22=0+1.88\cdot t \\ \\ t=(32.22)/(1.88) \\ \\ t=17.14\text{ s} \\ \end{gathered}`