# Free fall, problem,

1. Sep 24, 2010

### kalupahana

Free fall, problem, plz help

1. The problem statement, all variables and given/known data
A hoist is lifting a naturalist to the top of a cliff at 2.03 m/s vertically. The naturalist suddenly realizes she has left her pet rock behind. A friend picks it up and tosses it straight upward. If the naturalist is 2.50 m above her friend, what is the minimum initial speed the pet rock must have to reach the naturalist?
(consider gravitational acceleration as 10ms-2 & air resistance negligible)

2. Relevant equations
s = ut + ½ at2
v= u + at
v2 = u2 + 2as

Here u is initial velocity & v is final velocity

3. The attempt at a solution

The information of problem as follows
.........The hoist........................pet rock
u .........2.03................................. ?
v.........2.03................................. ?
s .........2.5 + x........................2.5 + x
t ...........?................................. ?
a.........non.................................-10

the both time & displacement should be equal

So the displacement of hoist
2.5 + x

The get minimum initial velocity the final velocity should be 0.
v = u + at
0 = u - 10t
t = u/10

the u is equal to

v2 = u2 + 2as
u2 = 20(2.5+x)

the displacement is equal to

s = ut + ½ at2

2.5 + x = ut - 5t2

What is the time of hoist when pet rock reach

2.5 + x = 2.03t
t = (2.5 + x)/2.03

or

x = 2.03t
t = x/2.03

which one i should take

2. Sep 24, 2010

### rock.freak667

Re: Free fall, problem, plz help

Well I would try to use conservation of energy.

When the naturalist is at the height 2.50m she is traveling at 2.03m/s, so she has a total energy associated with that. Now in order for the rock to reach that high, it must be imparted with kinetic energy equal to her total energy at that height.

3. Sep 24, 2010

### jmb88korean

Re: Free fall, problem, plz help

If you're looking for the absolute minimum initial velocity, then at the end its velocity will be zero because at the apex of its flight the rock will be stationary for a split second where the naturalist can grab it.

4. Sep 25, 2010

### The legend

Re: Free fall, problem, plz help

WOW!!
I had previously approached the prob a bit like kalupahana(and got the answer) did but this is much better!
Thanks!!

5. Sep 25, 2010

### rock.freak667

Re: Free fall, problem, plz help

Normally, for these kinds of problems, I try to use conservation of energy unless I am directly asked to find a time parameter.