Awildlife researcher is tracking a flock of geese. the geese fly 3.5 km due west, then turn toward the north by 40 ∘ and fly another 4.5 km, what is the magnitude of their displacement

To solve this problem, we can use the cosine formula for calculating the length of the displacement:

c^2 = a^2 + b^2 – 2 a b cos θ

where c is the displacement, a = 3.5 km, b = 4.5 km, and θ is the angle inside the triangle

Since the geeze turned 40° from west to north, so the angle inside the triangle must be:

θ = 180 – 40 = 140°

c^2 = 3.5^2 + 4.5^2 – 2 (3.5) (4.5) cos 140

c^2 = 56.63

c = 7.53 km

So the magnitude of the displacement is 7.53 km

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.

3. dark matter

empty space could also be a simple vacuum