Aseaplane flies horizontally over the ocean at 50 meters/second. it releases a buoy, which lands after 21 seconds. what's the vertical displacement from the plane to the ocean? (note: displacement will end up negative, since the direction is down.)

The motion of the buoy is a composition of two independent motions:
- a uniform motion on the horizontal axis, with constant speed vx=50 m/s
- an uniformly accelerated motion on the vertical axis, with constant acceleration 

Since we want to find the vertical displacement, we are only interested in the vertical motion.
The law of motion on the vertical direction is given by:

where
h is the initial height of the buoy
is the initial vertical velocity of the buoy, which is zero
t is the time

We know that the buoy lands after t=21 seconds, this means that the vertical position at t=21 s is y(21 s)=0. If we substitute these data into the equation, we can find the value of h, the initial height of the buoy:


And this corresponds to the vertical displacement of the buoy.

Liquid. good luck : )