Answer to Question #129455 in Classical Mechanics for Abdul Manan

Question

Passengers in PIA flight 123 that is flying west at speed of 900km/h observes F-16 flying for 14August parade rehearsal that passes the PIA plane horizontally 60° southwest direction. Peoples in PIA plane feels that F-16 moving away from them at 70° angle. Determine the true velocity of F-16. 

Answer 1

As per the given question,

Velocity of the flight 123 $(v)=-900\hat{i}$

Let the velocity of the F-16 is $(v_2)=-v\cos60\hat (i)-v\cos (60)\hat{j}$

observed angle with respect to flight 123$=70^\circ$

Hence, $\tan (70^\circ) =\frac{-v\sin (60^\circ)}{-900-v\cos(60^\circ)}$

$\Rightarrow 2466 -v\cos (60^\circ) =- v\sin 60^\circ$

$\Rightarrow v=\frac{2466}{\cos 60- \sin 60}=6737km/hour$