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Physics/Relativity

Question

QUESTION NO.1 The velocities of airplanes A and B are measured with respect to a frame of reference S fixed to the ground. Airplane A is traveling northeast (45 ͦ measured counter clockwise from the x axis) with a speed v_A= 140 m/s and airplane B is traveling southeast (45 ͦ measured clockwise from the x-axis) with a speed v_B=200 m/s. (a) What are the x and y components of each velocities? (b) Find the velocity v_A/B, which is the velocity of A as measured by B.

QUESTION NO.2 An observer notices that a moving clock runs slow by a factor of exactly 10. What is the speed of the clock?

Components of Plane A:
Vax=Va*cos(45)=99i
Vay=Va*sin(45)=99J
Components of Plane B:
Vbx=Vb*cos(-45)=141i
Vby=Vb*sin(-45)=-141j
The relative velocity is equal to the difference in the 2 velocities as measured from Plane B:
Vab=Va-Vb=[99i+99j]-[141i-141j]=-42i+240j
The magnitude of which can be determined from the Pythagorean Theorem:
Vab=sqrt[42^2+240^2]=244m/s
And the direction using the tangent:
alpha=atan(240/-42)=-80o=80oNW
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Physics