A cat chases a mouse across a 1.1 m high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor 1.6 m from...

Hello!

Denote the initial speed of the cat as The direction of the initial velocity is horizontal (assuming the table is horizontal). Denote the height of the table as and the given distance (horizontal) as  

After sliding, the cat participates in two movements which we can consider separately. The first is the horizontal one with the constant speed (there is no force to change this speed). The second is the vertical one (downwards) under the gravity force.

So the horizontal distance from the table is the height is  From the first equation we can find the time  The cat hits the floor at this moment, so must be zero. This gives the equation or

Solve this equation for    or   In numbers it is about 3.38 (m/s). This is the answer.

Note: if the given distance of is not a horizontal one but is the distance between the edge points of a cat's trajectory, then by the Pythagorean Theorem.