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

Vnd = 3.9 j

Vnp = 1.3 i

vpd = vpn + vnd

Vpd = -vnp + Vnd

Vpd = -1.3i + 3.9 j

speed = sqrt(1.3^2+3.9^2) = 4.11 m/s

direction = tan^-1(-1.3/3.9) = 18.43 north of west

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