SOLUTION: help please!!! Can you explain this step by step? if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any t

Question 764112: help please!!! Can you explain this step by step?

if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time is given by:
h=-16t^2+vt+s (where h and s are in ft, t is in seconds, and v is in ft/sec)
if a rock is thrown upward from a height of 100ft, with an initial velocity of 32ft/sec, solve for the time that it takes for it to hit the ground. (when h=0)
answer in seconds.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time is given by:
h=-16t^2+vt+s (where h and s are in ft, t is in seconds, and v is in ft/sec)
if a rock is thrown upward from a height of 100ft, with an initial velocity of 32ft/sec, solve for the time that it takes for it to hit the ground. (when h=0)
answer in seconds.
--------------
h=-16t^2+vt+s
---
h(t) = -16t^2 + 32t + 100
-16t^2 + 32t + 100 = 0
Solve for t

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=7424 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.69258240356725, 3.69258240356725. Here's your graph:

-----
t =~ 3.6926 seconds
Ignore the negative solution

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