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

Explanation:

V(N, D) = 4.9 j

V(N, P) = 1.7 i

The relative velocity between the above vectors is

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

The magnitude is

The unit vector is

The angle is

The angle is

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.