Re: Algebra/Physics problem
mathkid3 said:
A light plane must reach a speed of 33 m/s for takeoff. How long must the runway be if the plane has a constant acceleration of 3.8 m/s2 ?so, I am new to kinomatic equations. We are using the 4 Basic ones.
need to see this one worked out if I may.Thanks
I think the OP meant the kinematic equations, 4 basic ones meaning:
1) x=x
0+V
0t+1/2at
2
2) V=V
0+at
3) a=constant
4) V
2=V
02+2a(x-x
0)
If this is the case, the answer is a matter of determining starting values.
We can assume that the plane starts off at point 0 on the runway meaning that x
0=0. we can also assume that the plane's initial velocity is 0, V
0=0 (before moving). now we are given the acceleration, a=3.8m/s
2, and final velocity, V=33m/s. From this we can find how long it will take the plane to reach the final velocity, using equation 2:
33m/s=0+(3.8m/s
2)t
t=(33/3.8)s
Now that we have a value for t, we can use equation 1 to find the total runway length, x, required to reach takeoff speed:
x=0+0(t)+1/2at
2
=(1/2)(3.8m/s
2)((33/3.8)s)
2
=143.30m
therefore the minimum amount of runway needed to reach the plane's necessary takeoff speed is 143.30 meters.