calculate when displacement are equal

ahmedb

1. The problem statement, all variables and given/known data

One stone is dropped from the the top of a tall cliff, and a second stone with the same mass is thrown vertically from the same cliff with a velocity of 10.0 m/s [down], 0.50seconds after the first. Calculate the distance below the top of the cliff at which the second stone overtakes the first?

2. Relevant equations
v=0
d= -1/2(a)(t)^2

v=10
d=10(t)-1/2(a)(t)^2

3. The attempt at a solution

we have two unknowns, how can we solve it?!?!

SammyS

The time in this equation should be (t - 0.50), if t is the time in the previous equation .
Two equations in two unknowns.

ahmedb

i still don't get the answer, can you explain the steps please

SammyS

First rewrite the second equation,

d=10(t)-1/2(a)(t)² ,

using (t - 0.5) in place of t. (This is because the second stone is in the air for 1/2 second less time than the first stone.)

Then "FOIL" the (t - 0.5)², multiply out everything in the expression and then collect terms.

See what you have then.

ahmedb

so after you foil, you make the displacement equal to each other, and then solve for t, and then plug "T" into the original equation?

SammyS

Yes.

ahmedb

can you also do: d= -1/2(a)(t+.5)^2

cas the ffirst stone is .5 seconds in air longer than the second stone

SammyS

You can do either

t for the first stone and (t - 0.5) for the second stone,

OR

(t - 0.5) for the first stone and t for the second stone,

but not both (t + 0.5) and (t - 0.5).

ahmedb

don't you mean "t for the first stone and (t "+" 0.5) for the second stone,"?

SammyS

No. No matter how you express the time for each stone the time for the second stone is always 0.5 s less than the time for the first stone.

Therefore, the time for the first stone is always 0.5 s more than the time for the second stone.

ahmedb

(t - 0.5) for the first stone and t for the second stone,

for that cas the time for the first one is 5 less than the time for the second stone.

so is this correct "(t + 0.5) for the first stone and t for the second stone,"?

SammyS

Then, while the first stone falls for say 1 second, the the second stone would fall for 1 + 0.5 seconds. That's just not correct.

ahmedb

ohh lol, now i get it, thanks :D