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 1.10 m/s due east. What is Pauli's velocity relative to Daniel, ????⃗ PD?

Answer 1

4.05 m/s

Step-by-step explanation:

We shall represent the different velocity in vector form

Newton runs due north at 3.90 m/s, with respect to standing Daniel .

V_n = 3.9 j

Let Pauli runs with respect to standing Daniel with velocity X .

Then relative velocity of Newton with respect to running Pauli will be

3.9 j - X

Give that

relative velocity of Newton with respect to running Pauli = 1.1 i ( 1.1 due east )

So

3.9 j - X = 1.1 i

X = -1.1 i + 3.9 j .

Magnitude of X

X² = 1.1 ² + 3.9²

X = 4.05 m/s

So Pauli runs with respect to standing Daniel with velocity 4.05 m /s .

Direction will be , west of north at angle θ ,

Tan θ = 1.1 / 3.9