SOLUTION: Suppose someone threw a stone off a 100 m cliff. The height of the stone, h(t), in metres, after t seconds can be represented by the function {{{ -4.9t^2+3t+100=h(t) }}}. How long

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Suppose someone threw a stone off a 100 m cliff. The height of the stone, h(t), in metres, after t seconds can be represented by the function {{{ -4.9t^2+3t+100=h(t) }}}. How long       Log On


   

Question 940148: Suppose someone threw a stone off a 100 m cliff. The height of the stone, h(t), in metres, after t seconds can be represented by the function +-4.9t%5E2%2B3t%2B100=h%28t%29+. How long would it take for the stone to hit the ground?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
+-4.9t%5E2%2B3t%2B100=h%28t%29+.
+-4.9t%5E2%2B3t%2B100=+0+ (tossing out negative solution for unit measure)
t = 4.83402198619057 sec
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B3x%2B100+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A-4.9%2A100=1969.

Discriminant d=1969 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+1969+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+1969+%29%29%2F2%5C-4.9+=+-4.22177708823139
x%5B2%5D+=+%28-%283%29-sqrt%28+1969+%29%29%2F2%5C-4.9+=+4.83402198619057

Quadratic expression -4.9x%5E2%2B3x%2B100 can be factored:
-4.9x%5E2%2B3x%2B100+=+-4.9%28x--4.22177708823139%29%2A%28x-4.83402198619057%29
Again, the answer is: -4.22177708823139, 4.83402198619057. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B3%2Ax%2B100+%29