A river flows due south with a speed of 5.00 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.00 m/s due east. The river is 780 m wide. Part A What is the magnitude of his velocity relative to the earth

6.4 m/s

Explanation:

From the question, we are given that

Speed of the river, v(r) = 5 m/s

velocity relative to the water, v(w) = 4 m/s

Width of the river, d = 780 m

The magnitude of his velocity relative to the earth is v(m)

v(m) can be gotten by using the relation

[v(m)]² = [v(w)]² + [v(r)]²

[v(m)]² = 4² + 5²

[v(m)]² = 16 + 25

[v(m)]² = 41

v(m) = √41

v(m) = 6.4 m/s

thus, the magnitude of the velocity relative to earth is 6.4 m/s

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.