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 3.90 m/s, but from Pauli\'s point of view, Newton appears to be moving at 1.90 m/s due East. What must Pauli\'s velocity relative to Daniel be for this to be true? Give your answer in unit vector notation, where North is taken to be the positive y-direction and East is the positive x-direction. Next, express your answer as a magnitude and an angle measured counter-clockwise from due East.

Answer 1

a)
vND (Velocity of newton with repect to daniel) = 3.9 y m/s
vPD (Velocity of Pauli with repect to daniel) = ?
vNP (Velocity of newton with repect to pauli) = 1.9 x m/s
use:
vNP = vND - VPD
1.9 x = 3.9 y - vPD
vPD = 3.9 y - 1.9 x

b)
Magnitude = sqrt(3.9^2 + 1.9^2) = 4.34 m/s
Since x is negative and y is positive, vector lies in North-west cordinate.
Angle = 90 + atan (1.9/3.9)
= 90 + 26
= 116 degree