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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 4.90 m / s, but from Pauli's point of view, Newton appears to be moving at 1.70 m / s due east. What is Pauli's velocity relative to Daniel, → v PD ? Give your answer in unit vector notation, where north is taken to be the positive y - direction and east is the positive x - direction. → v PD = a ^ ı + b ^ ȷ

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Answer:

[tex]0.327\hat{i}+0.94475\hat{j}[/tex]

Explanation:

V(N, D) = 4.9 j

V(N, P) = 1.7 i

The relative velocity between the above vectors is

[tex]V(P, D)=V(N, D)-V(N, P)\\\Rightarrow V(P, D)=4.9j-1.7i[/tex]

So x component is -1.7 m/s and y component is 4.9 m/s

The magnitude is

[tex]\sqrt{(-1.7)^2+4.9^2}=5.18652099196\ m/s[/tex]

The unit vector is

[tex]-\dfrac{1.7}{5.18652099196}i+\dfrac{4.9}{5.18652099196}j=-0.327\hat{i}+0.94475\hat{j}[/tex]

The angle is

[tex]tan^{-1}\dfrac{4.9}{2.1}=66.8^{\circ}=180-66.8=113.2^{\circ}[/tex]

The angle is [tex]113.2^{\circ}[/tex]

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