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Polikarpov's aeroplane required for take-off a speed of 80km/hr, the run on the ground being 100m. The weight of the aeroplane was 1000kg-wt and the coefficient of friction between the aeroplane and the ground may be taken as 0-2. What should be the minimum power of the engine for the aeroplane to take off under these conditions? Assume that the plane accelerates uniformly during the take-off.

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The maximum power should be developed by the motor at the end of the take-off, and should be equal to N = Fv, where F is the thrust of the propeller — assumed to be constant during the take-off. 

The force F is determined from the equations for Newton's second law for the take-off:

 F—kP — Pa/g

where P is the weight of the aeroplane and k the coefficient of friction; the acceleration a is v2/25, from which it follows that

and the power is

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