# Question:Help with a little assignment

## Question:Help with a little assignment

Maple 18

Hi,

Im new to Maple and have a hard time trying to get used to it. I've understood the basics, but I have still trouble with solving more complex exercises.

The assignment:

In the lectures it was discussed that the air resistance of a body moving with velocity v may be written:

FD(v) =1/2*C*p*A*v^2 . (1)

with a drag coefficient C which is almost constant on a wide range of Reynolds numbers. Here p  is the density of the air. In most contexts, A is the bodies cross-sectional area, but for aircraft it is common to use instead the wing’s area. The drag force is directed opposite to the direction of motion. For a asymmetric bodies such as the wings of an aircraft, additional forces, such as the lifting force, which is perpendicular to the direction of motion, appear. It may be written written in a form similar to (1):

FL(v) =1/2*CL*p*A*v^2 . (2)

Here A is the area in the lift direction, here the wing area for the aircraft. The lift coefficient CL is approximately constant over a wide range of Reynolds numbers.

a) When an aircraft flies horizontally, the lift force FL must balance the force of gravity mg, where m is the aircraft’s mass and g = 9.81m/s2 the gravitational acceleration. Compute the velocity, v0, of a sport airplane at an altitude of h0 = 1 000m, where air’s density is  p= 1.10 kg/m3. The plane has mass m = 750 kg, wing area A = 18m2 and lift coefficient CL = 0.35 .

b) The propeller of an aircraft transmits power from the engine to the surrounding air. This power is used entirely to overcome the drag force. Compute the engine’s power P0 = FDv of the sport plane when it flies at a velocity v = v0 if the drag coefficient (based on the wing area) is C = 0.030.

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