PLEASE HELP!!!! will give MAD KARMA POINTS!!!!! and my undying gratitude Drag on

Question

PLEASE HELP!!!! will give MAD KARMA POINTS!!!!!
and my undying gratitude

Drag on a flying airplane is not simple. One model says thatthe total drag will have the form
Fd = v2 +/(v2), where and are positive constants that depend on the shapeand size of the airplane and the density of the air. For aCessna 150,
= 0.30 Ns2/m2 and = 3.5 x 105Nm2/s2.    In steady flight (constant velocity), the engine must provide aforward force that exactly balances the drag.

(a) Find a symbolic expression for the speed at which an airplanewith this drag force will have the maximum range for the givenquantity of fuel.

(b) Plug in numbers for the Cessna to find speed inkm/hthat maximizes the range.

(c) Find a symbolic expression for the speed atwhich an airplane with this drag force will have a maximum flighttime (remain in the air the longest time)

(d) Plug in numbers for the Cessna to find the speed inkm /h that maximizes theflight time.

thanks a lot

Explanation / Answer

I got it ! It hit me like a 5 tonne water balloon thrown by apirate-leprechaun! Obviously, for most time we need least deceleration. Which means weneed least drag force. So we just have to find the minimum value ofF=v2 + /v2ma=v2+ /v2 (anda=v/t) mv/t=(v4 + )/v2mv3/t=(v4 + ) t=mv3/(v4 +) differentiating to get max valuefor t:     d/dt=(v4 +)*3mv2-mv3(4v3)/(v4+ )2     equating it to zero: (v4 +)*3mv2=mv3(4v3) 3v4+ 3=4v4 v4=3 v=4(3/)=43.25m/s 43.25 m/s =155.7 km/h I expect that "undying gratitude" now please.

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