Hi I need help with this question:
A steam catapult aboard an aircraft carrier can accelerate an F-18 Hornet so that its velocity is given by
v(t) = 104.85t feet/second
If the jet reaches its take-off velocity of 173 miles per hour at the end of the runway, how long does it take for the jet to take off?
How long is the runway?
I figured out that I needed to convert mph to feet per second which is:
173mph to 253.7333 fps
And this is where I get stuck I don't know what to do.
v(t) = dS/dt
v(t), read "v of t" or "v as a function of t", is velocity.
S is distance
t is time
So, as given,
dS/dt = 104.85t
Multiply both sides by dt,
dS = 104.85t dt
Integrate both sides,
S = (104.85)[(t^2)/2]
Hence if t = 2.41996 sec,
S = (104.85 /2)(2.41996^2) = 307 ft., the length of the runway ---answer.
If you want to check that via linear kinematics or physics,
You know distance is (average speed) times time
d = [(v1 +v2)/2]*t
v1 = initial speed = 0
v2 = speed at takeoff = 253.7333 ft/sec
t = 2.41996 sec
d = [(0 +253.733)/2]*(2.41996) = 307 ft. ---same.