The height in feet, h, reached by a projectile after t seconds is given by the function:

h(t) = -16t2 + 110t + 5

During what time interval did the projectile reach an altitude of at least 135 ft?

Question

The height in feet, h, reached by a projectile after t seconds is given by the function:

h(t) = -16t2 + 110t + 5

During what time interval did the projectile reach an altitude of at least 135 ft?

mathstudent55 · Answer

You want the height to be at least 135 ft.
Is "at least 135 ft" greater than of equal to 135 ft or is it less than or equal to 135 ft?

stephanieelizzz · Answer

It would be greater than or equal to 135?

stephanieelizzz · Answer

@mathstudent55

mathstudent55 · Answer

Correct.
Now set your expression greater than or equal to 135 and solve for t.

mathstudent55 · Answer

$-16t^2 + 110t + 5 \ge 135$

stephanieelizzz · Answer

Would you factor out first and then put them equal to zero?

mathstudent55 · Answer

Subtract 135 from both sides.
Then treat it as an equation by setting it equal to zero.
Use the quadratic formula to find values of t.

mathstudent55 · Answer

$-16t^2 + 110t - 130 \ge 0$

Solve for t:

$-16t^2 + 110t - 130 = 0$

mathstudent55 · Answer

You can divide both sides by -2, if you'd like to work with smaller numbers.
Then use the quadratic formula.

$8t^2 - 55t + 65 = 0$

mathstudent55 · Answer

$\Large x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

$\Large t = \dfrac{-(-55) \pm \sqrt{(-55)^2 - 4(8)(65)}}{2(8)} $

$\Large t = \dfrac{55 \pm \sqrt{3025 - 2080}}{16} $

$\Large t = \dfrac{55 \pm \sqrt{945}}{16} $

$\Large t = 1.52$   or   $t = 5.36$

mathstudent55 · Answer

The interval is between the two times above.