Question

You are designing an airport for small planes. One kind of aeroplane that might use this airfield must reach a speed before take-off of at least 100 km/h, and can accelerate constantly at 2 m/s2. If the runway is 150 m long, can this airplane reach the required speed for take-off? If not, what is the minimum distance that the runway should have?

Answer 1

Solution-

Using 3rd equation of motion we will find the final velocity at the end of the runway-

here u=0; a=2; s= 150

the equation is-

${v}^{2} = {u}^{2} + 2as$

so v=√0+2*2*150

v= √600 = 24.49 m/s

and required speed is 100*5/18 = 27.78 m/s

so this runway is not enough as we are getting to a sleed of 24.49 m/s which is less than the required.

Now, the required length of runway-

27.78^2 = 0 + 2*2*s

s = 771.72/4= 192.93m

Hope that satisfies you!!!