Aprofessional diver steps off of a cliff that is 18 m high. draw a sketch of the cliff, defining your origin and final position. (careful with negative and positive signs.) unlike the wb assignment, assume the diver jumps up first and has an initial vertical velocity is 4 m/s. (ignore air resistance.) (a) how long does it take the diver to hit the water? (b) what's the diver's velocity on impact with the water? (careful with negative and positive signs.)

19.2 m/s

Explanation:

We set a frame of reference with the origin at the cliff top and the positive X axis pointing down.

Then the initial position is:

X0 = 0

The initial speed is:

V0 = -4 m/s

It is negative because it is speed upwards and the frame of reference is positive downwards.

Since the diver is in free fall, he is affected only by the acceleration of gravity, we can consider him moving under constant acceleration:

X(t) = X0 + V0 * t + 1/2 * a * t^2

He will hit the water at X = 18 m, so:

18 = 0 - 4 * t + 1/2 * 9.81 * t^2

4.9 * t^2 - 4 * t - 18 = 0

Solving this equation electronically:

t = 2.37 s

The diver will hit the water 2.37 s after jumping.

The equation for speed under constant acceleration is:

V(t) = V0 + a * t

V(2.37) = -4 + 9.81 * 2.37 = 19.2 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.

i would say