SOLUTION: I came across this question, and I got completely stuck. Please help? "A ball is thrown downward with an initial velocity of 21 meters per second from a cliff that is 90 meters h

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I came across this question, and I got completely stuck. Please help? "A ball is thrown downward with an initial velocity of 21 meters per second from a cliff that is 90 meters h      Log On


   

Question 748269: I came across this question, and I got completely stuck. Please help?
"A ball is thrown downward with an initial velocity of 21 meters per second from a cliff that is 90 meters high. The height of the ball is given by the quadratic equation h=-4.9t^2-21t+110 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 60 meters from the ground. Round your answer to the nearest tenth of a second."
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h=-4.9t^2-21t+110
------
h(t) = -4.9t^2 - 21t + 90 It starts at 90 m high, h(0) = 90, not 110
h(t) = -4.9t^2-21t + 90 = 60 solve for t
-4.9t^2 - 21t + 30 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B-21x%2B30+=+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=%28-21%29%5E2-4%2A-4.9%2A30=1029.

Discriminant d=1029 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+1029+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+1029+%29%29%2F2%5C-4.9+=+-5.41612549639703
x%5B2%5D+=+%28-%28-21%29-sqrt%28+1029+%29%29%2F2%5C-4.9+=+1.13041121068274

Quadratic expression -4.9x%5E2%2B-21x%2B30 can be factored:
-4.9x%5E2%2B-21x%2B30+=+%28x--5.41612549639703%29%2A%28x-1.13041121068274%29
Again, the answer is: -5.41612549639703, 1.13041121068274. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B-21%2Ax%2B30+%29

===================
Ignore the negative solution
t = 1.13 seconds