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 3.65 m/s, but from Pauli's point of view, Newton appears to be moving at 1.70 m/s due East. What must Pauli's velocity relative to Daniel be for this to be true? Express your answer in terms of the x and y components 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

For Newton to appear to Pauli to be moving straight East, there must be no North or South component of relative motion between them. That means that Pauli has a northward component of motion exactly equal to Newton's pace of 3.65 m/s.

As Newton has no East or West component to his motion relative to the stationary Daniel, If Pauli sees Newton as moving to the East, then Pauli herself MUST be moving to the West at the observed rate of 1.70 m/s

so relative to Daniel, Pauli has a motion of -1.7i + 3.65j

v = (-1.7)² + 3.65²)
v = 4.03 m/s

and the angle of Pauli's motion relative to East is

tan = 3.65 / -1.7
= 114.97°

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