Answer:
The runway should be at least 0.27 km long.
Explanation:
Hi there!
The equations for position and velocity of the plane at a given time "t" are as follows:
x = x0 +v0 · t + 1/2 · a · t²
v = v0 + a · t
Where
x = position at time "t".
x0 = initial position.
v0 = initial velocity.
t = time.
a = acceleration.
v = velocity at time "t"
Let´s place the origin of the frame of reference at the point where the plane starts traveling to take off (x0 = 0). Since the plane starts from rest, v0 = 0.
First, using the equation of velocity, let´s find how much time it takes the plane to reach a velocity of 38 m/s.
v = v0 + a · t
38 m/s = 0 m/s + 2.8 m/s² · t
38 m/s / 2.8 m/s² = t
t = 14 s
Now, let´s find how much distance the plane travels in that time using the equation of position:
x = x0 +v0 · t + 1/2 · a · t²
x = 0 m + 0 m/s · t +1/2 · 2.8 m/s² · (14 s)²
x = 2.7 × 10² m
Then, the runway should be at least 0.27 km long.
Have a nice weekend!
