Question

The speed at which a light aircraft can take off is 120 km/h. (A) What is the minimum constant acceleration required for the plane to take off after it has run 240 meters? (B)How long does it take to take off?

Ps. I want a solution. For reference, The answer is ..(a)2.32m/s^2 (b) 14.4s

Answer 1

A) a = 2.31[m/s^2]; B) t = 14.4 [s]

Step-by-step explanation:

We can solve this problem using the kinematic equations, but firts we must identify the data:

Vf= final velocity = take off velocity = 120[km/h]

Vi= initial velocity = 0, because the plane starts to move from the rest.

dx= distance to run = 240 [m]

`v_(f) ^(2) =v_(i) ^(2)+2*g*dx\\where:\\v_(f)=120[(km)/(h) ]*(1hr)/(3600sg) * (1000m)/(1km) =33.33[m/s]\\\\Replacing\\33.33^(2)=0+2*a*(240)\\ a=(11108.88)/(2*240)\\  a=2.31[m/s^2]\\`

To find the time we must use another kinematic equation.

`v_(f) =v_(i) +a*t\\replacing:\\33.33=0+(2.31*t)\\t=(33.33)/(2.31)\\ t=14.4[s]`