The displacement vector from your house to the library is 760 m long, pointing 35° north of east. what are the components of this displacement
vector?

The two components of displacement vector are:

Explanation:

Given:

The magnitude of displacement is 760 m.

The direction of the displacement vector is 35° North of East.

North of East means that the vector is between North and East and makes an angle of 35° with the east direction.

Now, there are two components of this displacement vector. One component is along the East direction and the other perpendicular to the East direction which is the North direction.

Component along the East direction is given as:

Component along the North direction is given as:

Therefore, the two components that are mutually perpendicular to each other are 622.56 m East and 435.92 m North.

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.

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer