SOLUTION: A ball is hit into the air from a height of 4 feet. The function g(t)=-16t^2+120t+4 can be used to model the height of the ball where t is the time in seconds after the ball is hi

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A ball is hit into the air from a height of 4 feet. The function g(t)=-16t^2+120t+4 can be used to model the height of the ball where t is the time in seconds after the ball is hi      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1170723: A ball is hit into the air from a height of 4 feet. The function g(t)=-16t^2+120t+4 can be used to model the height of the ball where t is the time in seconds after the ball is hit.
a.About how long is the ball in the air?
b.When is the ball back to 4 feet off the ground?
c.How high is the ball after 4 seconds?
d.When is the ball 150 feet in the air?
e.What is the maximum height the ball reaches? How many seconds does it take for this max to occur?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a. About how long is the ball in the air?
g%28t%29=0
0=-16t%5E2%2B120t%2B4
t=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
t=%28-120%2B-sqrt%28120%5E2-4%28-16%294%29%29%2F%282%28-16%29%29....
t=%28-120%2B-sqrt%2814656%29%29%2F%28-32%29
t=%28-120%2B-121.06%29%2F%28-32%29
need only positive solution
t=%28-120-121.06%29%2F%28-32%29
t ≅ 7.53seconds

b. When is the ball back to 4 feet off the ground?
g%28t%29=4
4=-16t%5E2%2B120t%2B4....simplify
1=-4t%5E2%2B30t%2B1
0=-4t%5E2%2B30t%2B1-1
0=-4t%5E2%2B30t
0=-4t%28t-30%2F4%29
0=-4t%28t-15%2F2%29
need only positive solution
0=%28t-15%2F2%29
t=15%2F2
t=7.5seconds

c. How high is the ball after 4 seconds?
t=4
g%284%29=-16%2A4%5E2%2B120%2A4%2B4
g%284%29=228 feet

d. When is the ball 150 feet in the air?
g%28t%29=150
150=-16t%5E2%2B120t%2B4
0=-16t%5E2%2B120t%2B4-150
0=-16t%5E2%2B120t-146
t=%28-120%2B-sqrt%28120%5E2-4%28-16%29%28-146%29%29%29%2F%282%28-16%29%29
t=%28-120%2B-sqrt%285056%29%29%2F%28-32%29
need only positive solution
t=%28-120%2B-71.1%29%2F%28-32%29
t=%28-120-71.1%29%2F%28-32%29
t=5.971875
t ≅ 5.97seconds

e. What is the maximum height the ball reaches? How many seconds does it take for this max to occur?
max is at vertex, write equation in vertex form
g%28x%29=-16t%5E2%2B120t%2B4....complete square
g%28x%29=%28-16t%5E2%2B120t%29%2B4
g%28x%29=-16%28t%5E2-%2815%2F2%29t%29%2B4
g%28x%29=-16%28t%5E2-%2815%2F2%29t%2Bb%5E2%29-%28-16b%5E2%29%2B4.......b=%2815%2F2%29%2F2=15%2F4
g%28x%29=-16%28t%5E2-%2815%2F2%29t%2B%2815%2F4%29%5E2%29-%28-16%2815%2F4%29%5E2%29%2B4
g%28x%29=-16%28t-15%2F4%29%5E2%2B16%28225%2F16%29%2B4
g%28x%29=-16%28t-15%2F4%29%5E2%2B225%2B4
g%28x%29=-16%28t-15%2F4%29%5E2%2B229
=>h=15%2F4 and k=229
vetex is at (15%2F4,229)
max is 229, and it will take 15%2F4 seconds for this max to occur