SOLUTION: a) a baseball player hit a very high pop-up ball. H is the height in meters given by h(t) = 1+30t-5t^2 and t is the time in seconds. What height does this ball not reach? b)if it

Question 1176831: a) a baseball player hit a very high pop-up ball. H is the height in meters given by h(t) = 1+30t-5t^2 and t is the time in seconds. What height does this ball not reach?
b)if it is caught at the height it was hit, how long is it in the air. Round off to one decimal place.
I'm quite confused on how I can solve these, as I did try using the quadratic equation and it didn't work.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
I'm assuming that the first part is what height does it reach. What it does not reach is everything else.
h(t)=-5t^2+30t+1
vertex is at x=-b/2a or -30/-10 or at 3 seconds for t
h(3)=-45+90+1 or 46 m height reached.
set that equation equal to 1
there are two places where h(t)=1, at the bat and when caught.
so h(t)=-5t^2+30t=-5t(t-6)=0
t=6.0 seconds, twice the time to get to the vertex, since this is symmetric at h(t)=1 m

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Introductory lesson on a projectile thrown-shot-launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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