I've been struggling with this for a while but despite my best efforts I have not been able to form suitable equations. Question is as follows:
A stone is dropped from a cliff $160 ~\text{ft}$ high and $\frac{1}{2}$ second later another stone is thrown vertically upwards from the base of the cliff at $64 ~\text{ft}~\text{sec}^{-1}$. Find the distance from the base of the cliff at which the two stones meet and their velocities at that moment.
I tried the following approach:
$$s_1=16t^2$$ $$s_2=64\left(t-\frac{1}{2}\right)-16\left(t-\frac{1}{2}\right)^2$$
where $$s_2=160-s_1$$
I don't think equations are correct but am not sure where I'm going wrong; the answer gives $60~\text{ft}$ for distance but I can't get this despite several attempts. I've done several questions where stones are released from the same position but not when they're in different positions. I don't know if this is a question in which relative motion can be used but I don't know how to approach the question if this is the case as velocities aren't constant. As always any advice would be greatly appreciated.