Say we shoot a missile in a purely vertical direction at an

Say we shoot a missile in a purely vertical direction at an initial velocity of 99 mph. Determine the max height (in ft) it will travel if the drag (in lb) on the missile is equal to [10.1 + 0.013 V^2], where v is the vertical velocity, in ft/sec. The missile weighs 2000 lb. To solve, you may need help from

Solution

given

velocity on misssile is, v = 99 mph = 99*(5280 feet/3600sec) = 145.2 ft/s

Drag on missile, D = 10.1+0.013v^2 (v is in ft/s) then

                           = 10.1+0.013(145.2)^2 = 284.2 lb = 284.2*4.448 = 1264.12 N

missile weigh, m = 2000 lb = 2000*0.453592 = 907.2 kg

Net Force on missile is

                                 F = -m*g - D = -(907.2*9.8)-1264.12 = 10,154.68 N

   But F = m*a then

                       a = F/m = -10,154.68/907.2 = -11.2 m/s^2

Since we know,

                                    v^2-u^2=2aS

here, v = final velocity = 0

        u = initial velocity = 145.2 ft/s = 145.2*0.3048 m/s = 44.26 m/s

       a = acceleration = -11.2 m/s^2

Then,

                  S = u^2/(2*a) = 87.45 m = 87.45*3.28084 = 286.91 ft