[Mechanics] Solving equations with 2 variables

[tigerd12]

Hello there, I am having a lot of trouble solving a question with which I cannot even begin, I have tried making 2 equations and equation, but I just end up with some number = 0, which is of course wrong, here is the question.

QUESTION

A stone is dropped from the top of a tower. One second later another stone is thrown vertically downwards from the same point with a velocity of 14ms^-1. If they hit the ground together find the height of the tower.

I've managed to get that..

First rock

s = ?
u = 0
v = ?
a = 9.8
t = ?

Second rock

s = ?
u = 14
v = ?
a = 9.8
t = ?

Now where do I go from here? I've tried making 2 equations using the same base equation i.e. v^2 = u^2 + 2as with the different values and then equating them, which doesn't work.

Any help would be much appreciated, thanks.

 

[HallsofIvy]

You haven't really shown much. Where did you get the formula v^2+ u^2+ 2as? "Conservation of energy".

I would just use the dynamics equations: If an object falls under gravity with initial velocity v, then s= -4.9t²+ vt is the distance it has fallen. The first rock has fallen, at time t, a distance h= -4.9t² and the second rock has has fallen a distance h= -4.9(t-1)²- 14(t-1). Those are negative because it is downward. The second equation has t-1 because the rock was thrown one second after the first rock so the time it has been falling is 1 less. Since the height, h, and the time, t, are the same for those two rocks, you can solve the two equations for h and t. h is what you are asked.