Thread: velocity question

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?

__________ seconds.

How long is the runway?
__________ feet

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.

Originally Posted by killasnake

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?

__________ seconds.

How long is the runway?
__________ feet

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=104.85 t ft/s.

Take-off speed is 253.733 ft/s, and so the plane reaches this speed
when:

104.85 t=253.733,

or:

t=253.733/104.85 seconds.

RonL

(aside: there is no such aircraft as the f-18, probably f/a-18 Hornet is meant)

Thank you for the help

You know, I read Malaygoel's post and whereas it wasn't very specific, it WAS the method for solving for the length of the runway. I wouldn't have called it "totally useless."

-Dan

Well, One more question

Now know how long the take off speed is which is 2.41996 How do I figure out how long the runway is?

Originally Posted by killasnake

Well, One more question

Now know how long the take off speed is which is 2.41996 How do I figure out how long the runway is?

Since you posted this in the Calculus section, you use the integration as suggested before.

v(t) = dS/dt
where
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

Here,
v1 = initial speed = 0
v2 = speed at takeoff = 253.7333 ft/sec
t = 2.41996 sec
So,
d = [(0 +253.733)/2]*(2.41996) = 307 ft. ---same.