Find the x and y components of a position vector r⃗ , of magnitude r = 78 m, if its angle relative to the x axis is 30.0 ∘.

Given: The magnitude of position vector r = r = 78 m

The angle relative to the x-axis θ =30°

Concept: If the position vector r making angle θ with x-axis then position vector can be expressed as

                              r = r cos θ i + r sin θ j

Here, i and j are the unit vectors along x and y axes respectively.

x component of position vector r = r cos θ

y component of position vector r = r sin θ

Solution: From the given problem, the position vector r can be written as

                          r = (78 cos 30° i + 78 sin 30° j ) m

So, the x component of position vector r = 78 cos 30° m = 67.55 m

And, the y component of position vector r = 78 sin 30° m = 39.0 m

Hence, the required x & y components of position vector r will 67.55 m and 39.0 m respectively.

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.