Instantaneous velocity and gravity

[thezakster]

a water balloon is thrown from a building

h(t)=-.5gt^2 + Vot + So

h=height of balloon above ground
t=time
g=32 ft/sec (gravity constant)
So= initial height
Vo= instantaneous velocity at t=0

balloon reaches apex at 100 feet, at t=1.5 sec, it hits the ground at t=4 sec

write an equation that gives the height of the balloon at t=0 by solving for the constants Vo and So

estimate instantaneous velocity at t=3, find average velocity over time interval [3,3+h]



I don't know where to start with this. How would I find the two constants

 

[tkhunny]

a water balloon is thrown from a building

h(t)=-.5gt^2 + Vot + So

h=height of balloon above ground
t=time
g=32 ft/sec (gravity constant)
So= initial height
Vo= instantaneous velocity at t=0

balloon reaches apex at 100 feet, at t=1.5 sec, it hits the ground at t=4 sec

write an equation that gives the height of the balloon at t=0 by solving for the constants Vo and So

estimate instantaneous velocity at t=3, find average velocity over time interval [3,3+h]

It seems as though we do NOT get to use derivatives, yet. That really is fine, on such a problem, since it can all be done with a little analytic geometry and algebra.

Put it in a form that exposes its structure: 4p(y-k) = (x-h)² Does that ring any bells? It should. If it doesn't, I strongly recommend you go find a book on Analytic Geometry and get up to speed. It will only get worse.

h(t)=-.5gt^2 + Vot + So = -½g(t² - V₀(2/g)*t + _____) + S₀ - ______

Complete the square -- fill in the blanks. This should make it easy to spot the vertex, which you will have to force to have a 100 ft in the vertical component.