Answer: V = 47.7 mi/hr
Explanation:
first we calculate elements of aero-dynamic resistance
Ka = p/2 * CD * A.f
p is the density of air(0.002378 slugs/ft^3) for zero altitude, CD is the drag coefficient(0.35) and A.f is the front region of the vehicle
so we substitute
Ka = 0.002378/2 * 0.35 * 18
Ka = 0.00749
Now we calculate the final speed of the vehicle (V2) using the relation;
S = (YbW/2gKa)In[ (UW + KaV1^2 + FriW ± Wsinθg) / (UW + KaV2^2 + FriW ± Wsinθg)
so
WE SUBSTITUTE
150 = (1.04 * 2700 / 2 * 32.2 * 0.0075) In [(0.8 * 2700 + 0.0075 *(78mil/hr * 5280ft/1min * 1hr/3600s)^2 + 0.017 * 2700 ± 2700 * 0.04) / (0.8 * 2700 + 0.0075 * V2^2 + 0.017 * 2700 ± 2700 * 0.04)]
150 = (2808/0.483) In [(2160 + 98.16 + 153.9) / ( 2160 + 0.0075V2^2 + 153.9)]
150 = 5813.66 In [ (2160 + 98.16 + 153.9) / ( 2160 + 0.0075V2^2 + 153.9)]
divide both sides by 5813.66
0.0258 = In [ (2412.06) / ( 0.0075V2^2 + 2313.9)]
take the e^ of both side
e^0.0258 = (2412.06) / ( 0.0075V2^2 + 2313.9)
1.0261 = (2412.06) / ( 0.0075V2^2 + 2313.9)]
(0.0075V2^2 + 2313.9) = 2412.06 / 1.0261
(0.0075V2^2 + 2313.9) = 2350.7
0.0075V2^2 = 2350.7 - 2313.9
0.0075V2^2 = 36.8
V2^2 = 36.8 / 0.0075
V2^2 = 4906.6666
V2 = √4906.6666
V2 = 70.0476 ft/s
converting to miles per hour
V2 = 70.0476 ft/s * 1 mil / 5280 ft * 3600s / 1hr
V = 47.7 mi/hr
