Ahiker climbs a mountain. starting at the base of the mountain, he first moved up 520m at a 32.0 degree angle. what is the final displacement of the hiker?

Explanation:

Displacement Vector

Suppose an object is located at a position  

and then moves at another position at

The displacement vector is directed from the first to the second position and can be found as

If the position is given as magnitude-angle data ( z , α), we can compute its rectangular components as

The question describes the situation where the initial point is the base of the mountain, where both components are zero

The final point is given as a 520 m distance and a 32-degree angle, so  

The displacement 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.