How Fast Must the Rock Be Thrown to Reach the Naturalist?

[kalupahana]

Free fall, problem, please help

Homework Statement

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)

Homework Equations

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

Here u is initial velocity & v is final velocity

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

from here i don't have any idea, please help me.

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

 

[rock.freak667]

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.

 

[jmb88korean]

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.

 

[The legend]

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.

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

 

[rock.freak667]

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

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