Question

You accidentally throw your car keys horizontally at 8.0 m/s from a cliff 64 m high. How far from the base of the cliff should you look for the keys?

Answer 1

I would use the equation Δx=vi*cos$\alpha$*t
(Keep in mind, because it is horizontal, the angle will be 0 degrees.)
The first thing you would need to find is the time
So, you would use Δy=1/2*a(Δt)²
Plug in what you know:
64=1/2*9.8t²
64=4.9t²
64/4.9=13.06
13.06=t²
√13.06=√t²
t=3.61sec

Now that you have t, you can plug it into this equation:
Δx=vi*cos$\alpha$*t
Δx=8*cos(0)*3.61
Δx=28.88

The keys travelled 28.88m from the cliff.
Hope this makes sense and it helps :)