In a local bar, a customer slides an empty beer mug down the counter for a refill. the height of the counter is 1.18 m. the mug slides off the counter and strikes the floor 1.20 m from the base of the counter.
with what velocity did the mug leave the counter?
what was the direction of the mug's velocity just before it hit the floor?

At first we have to find the time index, but you have to remember that time does not depend on mug's horizontal velocity. In this case : D=1/2∗g∗t2=1.18 where the in. velocity is 1.2/t.
Of course the mug velocity will be the same as previous one :
 v=g*t
Then we have  θ=tan−1(vy/vx) so that you can easily find what you need using trigonometry.

Ihope you get it right bro