12.10 Relative-Motion Analysis of Two Particles Using Translating Axes Relative Motion (Translating Axes) - Consider two particles A and B. Both are moving with respect to fixed axes X-Y - The translating axes x-y is moving with particle B - The position vector of the particle A measured relative to the x-y axes is (A/B means A with respect to B)

KINEMATICS OF PARTICLES If is the absolute position of B, then Take derivative with respect to time : or and or

A B 160 km/h 180 km/h

EXAMPLE The passenger aircraft B is flying east with velocity vB = 800 km/h. A jet is traveling south with velocity vA = 1200 km/h. What velocity does A appear to a passenger in B ? x y Solution

EXAMPLE (Cont.) Absolute value : The direction of y West of South x

Example q

Example

Problem At the instant shown, the car at A is traveling at 10 m/s around the curve while increasing its speed at 2 m/s2. The car at B is traveling at 18.5 m/s along the straightway and increasing its speed at 5 m/s2. Determine the relative velocity and relative acceleration of A with respect to B at this instant

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