An airplane is descending in a circular pattern that has a constant radius of 25

Question

An airplane is descending in a  circular pattern that has a constant radius of 250m. If the airplane has a horizontal speed of 75 m/s (constant) and a downward speed of 5 m/s (which is increasing at a rate of 2 m/s^2), determined the acceleration of the airplane.

An airplane is descending in a circular pattern that has a constant radius of 250m. If the airplane has a horizontal speed of 75 m/s (constant) and a downward speed of 5 m/s (which is increasing at a rate of 2 m/s^2), determined the acceleration of the airplane.

Explanation / Answer

Net downward acceleration= 2m/s^2

Net radial/horizontal acceleration = V*V/r= 75*75/250=22.5m/s^2

Hence, net acceleration of airplane =sqrt(2*2 + 22.5*22.5)

=22.58874

Angle made by acceleration vector with horizontal= tan inverse (2/22.5) = 5.079 degree

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