a jet aircraft has a takeoff mass of 120000 kg. Each of it's four engine has a net thrus of 75 KN. Calculate the acceleration and the length of the runway needed to become airborne if the takeoff speed is 73 m/s. (neglect any frictional forces and air- resitance)

Question

anonymous · Answer

Ignoring air resistance, friction and assuming an initial velocity of 0 (i.e. the jet is at standstill immediately before accelerating), and assuming the engines go from 0 to 75000N of thrust instantaneously.
$$\Large \begin{array}{l}
F = ma\
v = u + at\
s = ut + \frac{1}{2}a{t^2}\
F = 4 \cdot 75000 = 300000{\rm{ N}}\
a = \frac{F}{m} = \frac{{300000}}{{120000}} = 2.5{\rm{ m}}{{\rm{s}}^{ - 2}}\
t = \frac{{v - u}}{a} = \frac{{73-0}}{{2.5}} = 29.2{\rm{ s}}\
s = 0 + \frac{1}{2}2.5 \cdot {29.2^2} = 1065.8{\rm{ m}}
\end{array}$$

anonymous · Answer

what equations did you use?

anonymous · Answer

The equations are at the top, just the basic kinematic equations.

anonymous · Answer

but isn't in (S) in the third rule supposed to be  (D) displacment?

anonymous · Answer

It's the same thing. There's generally a few different co-efficients used to express the same variable - for example, v is sometimes v_f and u is sometimes v_i (for final velocity and initial velocity, respectively). s and d are both used for displacement.

anonymous · Answer

You could use batmanpinkelephant as a variable name if you so desired, so long as it was well-defined =)

anonymous · Answer

yah i just wondered because i'm used to d :))