A busy waitress slides a plate of apple pie along a counter to a hungry customer sitting near the end of the counter. The customer is not paying attention, and the plate slides off the counter horizontally at 0.84 m/s. The counter is 1.38 m high. a. How long does it take the plate to fall to the floor? b. How far from the base of the counter does the plate hit the floor? c. What are the horizontal and vertical components of the plate’s velocity just before it hits the floor?

First find out how long it would take the plate to hit the floor if it were simply dropped from the height of the counter instead of sliding off horizontally. That is a typical "falling body" problem. The vectors and forces involved in motion can be broken up into components. If you look at the y (i.e. vertical) components in this problem, it amounts to solving the problem for a dropped plate.

This is like the saying that a dropped bullet falls as fast as one fired horizontally from the same height. I think the Mythbusters tested that one.

a.) The acceleration in the Y direction is constant: g=9.80 m/s^2. You know the initial velocity in the y=0 (think about it) and that the counter is 1.38 m high, so find the time it takes to fall in the y "from rest" 1.38 m to the floor.

b.) As the plate leaves the table, velocity in the x is 0.84 m/s. Just multiply (0.84) * (time from part a). b/c Velocity in the x direction is constant.

c.) just draw the Vy and Vx velocity components as a triangle. Y points down and x points away from the counter.