A small aircraft requires a speed of 34.0 m/s in order to take off. What minimum constant acceleration does this require if the aircraft is to be airborne at the end of a 245. meter long runway?
I'm not sure how to set up the problem.
See previous post: Wed, 8-12-15, 9:20 PM.
To solve this problem, we can use the equation of motion:
v^2 = u^2 + 2as,
where:
v = final velocity (34.0 m/s, as the aircraft needs to be airborne at the end of the runway)
u = initial velocity (0 m/s, as the aircraft starts from rest and needs to reach a speed of 34.0 m/s)
a = acceleration (the value we want to find)
s = displacement (245.0 m, the length of the runway)
Rearranging the equation gives:
a = (v^2 - u^2) / (2s).
Now we can substitute the given values into the equation:
a = (34.0^2 - 0^2) / (2 * 245.0).
Evaluating this expression:
a = (1156.0) / (490.0).
Simplifying further:
a = 2.36 m/s^2.
So, the minimum constant acceleration required for the aircraft to be airborne at the end of the runway is 2.36 m/s^2.