Daniel takes his two dogs, Pauli the Pointer and Newton the Newfoundland, out to
ID: 1627316 • Letter: D
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 1.10 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
Velocity of newton with respect to Daniel VND = 3.65 j
Velocity of newton with respect to Pauli VNP = 1.1 i
Vevlocity of the pauli with respect to Daniel VPD = VND - VNP = 3.65 j - 1.1 i
VPD = -1.1 i + 3.65 j
Hence x component = -1.1 m/s
Y component = 3.65 m/s
Velocity = (1.12 + 3.652)1/2 = 3.81 m/s
For direction
angle = tan-1(Y component / x component) = 73.2287
From east it will be = 180 - 73.2287 = 106.771 degree
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