Daniel takes his two dogs, Pauli the Pointer and Newton the Newfoundland, out to

Question

Daniel takes his two dogs, Pauli the Pointer and Newton the Newfoundland, out to a field and lets them loose to exercise.  Both dogs sprint away in different directions, while Daniel stands still.  From Daniel's point of view, Newton runs due North at 3.40 m/s, but from Pauli's point of view, Newton appears to be moving at 1.30 m/s due East.  What must Pauli's velocity relative to Daniel be for this to be true?

Express your answer in unit vector notation if North is the  y-direction and East is the  x-direction, and then express your answer as a magnitude and an angle measured counter-clockwise from due East.

Explanation / Answer

v _ newton = 3.40 j   m/s

v_newton w.r.t to pauli = v_ newtoon - v_pauli

1.30 i   = 3.40j - vIpauli

v_ pauli = - 1.30i + 3.40 j     .........vector notation

magnitude = sqrt(1.30^2 + 3.40^2) = 3.64 m/s

angle = 180 - tan-1(3.40/1.30) = 110.92 degrees

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