This is Giancoli Answers with Mr. Dychko.
This garden hose sprays water straight up
and it's positioned 1.8 meters above the ground
and when the water launches from here,
it hits the ground 2.5 seconds later.
So the displacement of this water is gonna be negative 1.8 meters
if we choose upwards to be the position direction
and whenever in doubt about this negative or positive
for displacement, you can always think of displacement as being the final position
minus the initial position; typically, the letter y is used for this,
you know, the y-axis being vertical
so y final minus y initial and we have y final in this case being
zero if this is a zero level here
and then minus the initial position— minus 1.8 meters—above that
giving us negative 1.8 meters
so displacement is negative 1.8.
We'll use this formula to solve for the initial speed
and we'll subtract one-half at squared from both sides
and we get this next line after we switch the sides around
so that the unknown v i is on the left
and then divide both sides by t
and we get this formula for the initial speed.
So we plug in our numbers;
it's negative 1.8 meters displacement
minus one and a half times
negative 9.8 meters per second squared acceleration due to gravity
times 2.5 seconds square that
and divide by 2.5 for a total of 12 meters per second
it must have been the initial speed of the water.