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

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) (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.

RELATED QUESTIONS
82. sports- You throw a baseball straight up into the air a a velocity of 45 feet per... (answered by stanbon)

you throw a softball straight up into the air at a velocity of 30 feet per second. You... (answered by ikleyn)

SUPPOSE YOU THROW A BASEBALL STRAIGHT UP AT A VELOCITY OF 64 FEET PER SECOND. A FUNCTION (answered by stanbon)

A baseball player hits a baseball into the air from a height of 3 feet with an initial... (answered by ankor@dixie-net.com)

You arrive at a model rocket competition only to discover that you left your small solid... (answered by Alan3354)

You arrive at a model rocket competition only to discover that you left your small solid... (answered by ankor@dixie-net.com)

Again please help. Asked question earlier but didn't get a response. 3) Suppose you... (answered by venugopalramana)

a) 2) Suppose you throw a baseball straight up at a velocity of 32 feet per second. A... (answered by stanbon)

Please help. 3) Suppose you throw a baseball straight up at a velocity of 32 feet... (answered by venugopalramana)