For a project Mr Greens physics students made rockets During

For a project, Mr. Green\'s physics students made rockets. During class last week, the students launched their rockets from the bleachers of the school\'s outdoor football stadium. The bleacher location where Martin launched his rocket was 48 feet off the ground. The height of Martin\'s rocket in feet, t seconds after launch, is shown by the function below. h(t) = -16t^2 + 88t +48

Fill in the values below for the domain of this height function.

[ ], [ ]

-0.5, 0.0

0.0, 2.75

2.75, 6

6 , 40

40, 48

169 , 169

choose one from below : for this situation , the domain represents the rocket\'s:

1)total time in the air

2)original launch height

3)time to reach maximum height

4)maximum height Thank you!

Solution

minimum height of rocket is zero feet (i.e, on the ground), time cannot be negative , so t>= 0

h(t) = -16t² + 88t +48 >=0

=> 16t² - 88t -48 <=0

=>8(2t² -11t -6) <=0

=>2t² -11t -6 <=0

=>2t² -11t <=6

=>t² -(11_/2)t <=3

=>t² -(11_/2)t+(11_/4)² <=3+(11_/4)²

=>(t-(11_/4))²<=3+(11_/4)²

=>(t-(11_/4))²<=(169_/16)

=>(t-(11_/4))<=(13_/4)

=>t<=(24_/4)

=>t <=6

domain of this height function is [0.0,6]

for this situation , the domain represents the rocket\'s total time in the air