Help with free-fall physics question?

Question

I need help with the process or formula used for this problem:

A person jumps off a building 99.4 m high. They struck the ground at 39 m/s. How fast would they have traveled if there was no air resistance?

Answer 1

There's lots of equations. But you'll need to start with this one:

distance = 1/2 acceleration x time^2

...solving for time, that gives you...

time = sqrt ( 2 x distance / acceleration)

...of course you know the distance (99.4 m), and you know the acceleration of gravity (9.81 m/s^2).

Now, having figured out how long it takes this person to splat, you can vigure velocity:

velocity = acceleration x time

From that distance, he should have gotten pretty close to terminal velocity, so you should notice a pronounced difference.

Answer 2

The problem given is to find the speed at the bottom if an object is dropped from a height of 99.4 m assuming no resistance.

Since the initial speed is zero and height and acceleration are known.

Use the formula V^2 = U^2 + 2as.

Since U = 0 and a= g , V^2 = 2gs.

g = 9.8m/s^2 and s= 99.4m, V^2 = 2 x 9.8 x 99.4 = 1948.24

We get V= 44.1m/s.

Answer 3

Air resistance is generally an acceleration proportional to speed of object. Let's use k for the proportionality constant.

let a = acceleration (positive is downward)
g = gravity (positive in downward direction)
v (velocity)
Then you get:

a = g -kv

Note that the second term is negative, since the air resistance pushes something back upwards.

Then use the identity: a = dv/dt

and get:

dv/dt = g - kv

And then you re-read the question, and realize that you don't need to go through all this trouble, and use:

s = v^2/2g

This says that distance travelled is final velocity squared over twice the acceleration

Rearrange to get:

v = sqrt(2gs)

assume g is probably 9.81, s is 99.4m

This gives you:

V = 44m/s

This is final velocity, not average velocity or distance travelled, final velocity.

Answer 4

d = 99.4

d = 1/2 at^2

99.4 m = 1/2 * 9.8 m/s/s * t^2

t = sqrt(99.4/4.9) s

v = at

v = 9.8 * sqrt(99.4/4.9)

I get something close to 44.13887 m/s

I looked at some of the other answers. I don't think they were reading the question correctly. The answer to this one should be bigger than the velocity given in the problem with resistance.

Answer 5

Its very easy x=1/2at^2 x=99.4 a=9.8 and then t is 4.50 put it in v=at+v0 v=39 a=9.8 t=4.5 then v0 is -5
which means the wind velocity
now put v0=0 and solve it again
v=44.1 m/s

Answer 6

Do you need the speed at impact or the time of the fall?
If I recall properly: d = 1/2 at^2. Where d = distance, a = acceleration, and t = time.
a = 9.8 m/s/s.
Solve the equation for time.
If you need the speed of impact, v = at.

I'm sure someone will correct anything I got wrong.