A jet aeroplane of mass is flying horizontally due north at a constant speed of

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A jet aeroplane of mass

2.0\times10^{4}\,\text{kg}

is flying horizontally due north at a constant speed of

200\,\text{m\,s}^{-1}

. It then executes a level quarter-circle turn towards the east (radius of the turn

500\,\text{m}

) while maintaining the same speed throughout the manoeuvre. The turn is completed in

\dfrac{\pi r}{2v}

seconds, where

r

is the radius and

v

the constant speed. (i) Calculate the magnitude of the change in momentum of the aeroplane between the start and the end of the quarter-circle turn. (ii) Using the duration of the turn, determine the magnitude of the average horizontal force that must act on the aeroplane to accomplish the turn. (iii) Compare this average force with the weight of the aeroplane by finding the ratio

\dfrac{F_{\text{average}}}{mg}

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