SOLUTION: #82 Sports You throw a baseball straight up into the air at a velocity of 45 feet per second. You release the baseball at a height of 5.5 feet and catch it when it falls back to a

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: #82 Sports You throw a baseball straight up into the air at a velocity of 45 feet per second. You release the baseball at a height of 5.5 feet and catch it when it falls back to a      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 189179This question is from textbook College Algebra A Graphing Approach
: #82 Sports
You throw a baseball straight up into the air at a velocity of 45 feet per second. You release the baseball at a height of 5.5 feet and catch it when it falls back to a height of 6 feet.
a. Use the position equation to write a mathematical model for the height of the baseball.
b. Find the height of the baseball after 0.5 seconds.
c. How many seconds is the baseball in the air? Use a graphing utility to verify your answer. This question is from textbook College Algebra A Graphing Approach

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You throw a baseball straight up into the air at a velocity of 45 feet per second. You release the baseball at a height of 5.5 feet and catch it when it falls back to a height of 6 feet.
a. Use the position equation to write a mathematical model for the height of the baseball.
y = -16t^2 + 45t + 5.5 at any time t. y in feet, t in seconds
---------------------------
b. Find the height of the baseball after 0.5 seconds.
Sub 0.5 into the equation
y = -16*0.25 + 45*0.5 + 5.5
y = -4 + 22.5 + 5.5
y @ 0.5 = 24 feet
------------------
c. How many seconds is the baseball in the air? Use a graphing utility to verify your answer.
Find the times when the ball is at 6 feet. There are 2 of them, 1 going up, 1 coming down.
6 = -16t^2 + 45t + 5.5
16t^2 - 45t + 0.5 = 0
t = (45/32) - sqrt(1993)/32 (going up) and
t = (45/32) + sqrt(1993)/32 (coming down)
t = ~ 2.801 seconds
------------------------
The graph looks good.