Jetfighter Acceleration and Time

[Hurly]

Homework Statement

Calculate the acceleration (m/s^2) of a jet fighter which is launched from an aircraftcarrier by catapult, given the jet’s required takeoff speed (km/hr) and the distance available on deck to reach that speed (metres) as the catapult accelerates the jet from rest to takeoff. Assume constant acceleration.

You are also to calculate the time (secs) for the jet to be accelerated to takeoff speed. You are also required to report the acceleration in terms of its g-force where g = 9.80665m/s2.
where

- 304m Runway Distance
- 400 (km/hr) jet’s required takeoff speed

Need to Find out:

Calculate the acceleration (m/s^2) of a jet fighter which is launched from an aircraft-carrier by catapult - (from rest)

Calculate the time (secs) for the jet to be accelerated to takeoff speed

Homework Equations

Relevant formulae are (simple Newtonian motion with initial velocity of 0):
v = at
s = ½at^2

v = velocity, a = acceleration, t = time, s = distance.

The Attempt at a Solution

S = 0.5 * 304m * 400 km/hr * t^2

t^2 = 304 / 200 = 1.52

t = $\sqrt{304 / 200}$ = 1.2329

 

[CWatters]

Deleted as problem statement has been changed.

 

[CWatters]

If I'm correct I'd use the equation of motion...

V² = U² +2as

to calculate the acceleration.

 

[Hurly]

Sorry i fixed the question

- 304m Runway Distance
- 400 (km/hr) jet’s required takeoff speed

Need to Find out:

Calculate the acceleration (m/s^2) of a jet fighter which is launched from an aircraft-carrier by catapult - (from rest)

Calculate the time (secs) for the jet to be accelerated to takeoff speed

 

[CWatters]

In which case I've already given you one of the equations of motion to work out the acceleration "a"..

v² = u² +2as

u=0

so

V² = 2as

a = V²/2s

As for the time, here is another equation of motion...

s = ut + 1/2at²

u=0

so

s = 1/2at²

t = SQRT(2s/a)

I strongly recommend memorising the four basic equations of motion...

http://www.thestudentroom.co.uk/wik...Equations_of_Motion_for_Constant_Acceleration

v = u + at
s = 1/2(u+v)t
s = ut + 1/2at²
v² = u² +2as

 

[CWatters]

PS: Make sure to convert 400kph to m/S.

 

[Hurly]

Know values
Velocity of Jet Fighter 111.111 m/s

Distance of Runway = 360m


Calculations

a = $\frac{111.111^{2}}{2 x 360}$ = 17.14674211 m/s^-2


t = $\sqrt{\frac{2 x 360}{17.14674211}}$ = 6.480006480 Seconds

G-force = $\frac{17.14674211}{9.80665}$ = 1.748481093 G's


Pretty Sure this is correct