An airplane weighs 580000 lb with fuel and 100 passengers It

An airplane weighs 580,000 lb with fuel and 100 passengers. It takes off at 140 mph. What is the required take-off speed (units of mph) if it is loaded with 372 passengers and the same fuel as in the previous situation? Assume that each passenger and his/her luggage weighs 200 lb. Assume that the airplane has the same angle of attack, flap settings, etc. as in the 100-passenger case such that the lift coefficient is the same in both cases.

Solution

>> As, Velocity is directly proportional to Weight of aeroplane, under these conditions

>> Let, Weight of fuel = m

As, Each passenger weighs 200 lb

and, initially with 100 passengrs, total weight of aeroplane = 58000 lb

=> m + 200*100 = 58000

=> m = 38000 lb

>> Now, there are 372 passengers

So, total weight of aeroplane = 38000 + 200*372

=> Total Weight = 112400 lb

>> When Weight = 58000 lb, Velocity, V1 = 140 mph

When, Weight = 112400, Velocity, V2= ?

As, W1*V1 = W2*V2

=> V2 = 58000*140/112400

=> V2 = Final Velocity = 72.242 mph