A cat chases a mouse across a 1.3 m high table. The mouse steps out of the way, and the cat slides off the table. . .
and strikes the floor 2.1 m from the edge of the the table. What was the cat's speed when it slid off the table? the acceleration of gravity is 9.81 m/s^2. Answer in units of m/s.
The basis for answering this type of question is to understand that motion in the x-and y-directions are assumed to be independent.
The first thing is to determine how long it took for the cat to fall from the table top to the floor.
the basic equation is:
delta y = Viy + 1/2 gt^2.
At the moment the cat slid off the edge of the table, the velocity in the y-direction is assumed to be zero.
Then the equation simplifies to:
delta y = 1/2 gt^2.
delta y = 1.3 m, g = 9.81 m/s/s, and solve for t.
t = 0.515 s.
In that 0.515 s that the cat was falling, it was also moving horizontally a distance of 2.1 m.
v = d/t = 2.1/0.515 =4.08 m/s horizontal velocity as the cat left the table.