CPM Homework Help : A2C Problem 11-94

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Home > A2C > Chapter 11 > Lesson 11.2.4 > Problem 11-94

11-94.

For an object shot into the air, its height $h$ in feet above the ground after t seconds is given by the equation $h = 80t − 16t^{2}$ . Use this equation to answer the following questions.

For what times is the object on the ground?
Step 1 (a):
Substitute 0 for h.
80t − 16t² = 0
Answer (a):
It is on the ground at 0 and 5 seconds.
Step 2 (a):
Factor the equation.
16t(5 − t) = 0
For what domain is this function reasonable?

Hint (b):
When is the height positive?
Answer (b):
D: 0 ≤ t ≤ 5

How long did it take the object to hit the ground?

Hint (c):
At what time will the object be on the ground, not including when it starts?
Answer (c):
5 seconds

For what times is the height greater than $64$ feet?

Step 1 (d):
$16t ^{2} − 80t + 64 = 0$
Substitute 64 for h and solve for t.
Step 3 (d):
Factor the equation.
$\left(t − 1\right)\left(t − 4\right)$
Step 2 (d):
Simplify.
$t ^{2} − 5t + 4$
Step 4 (d):
$t = 1, 4$
Solve for t.
Step 5 (d):
Use these values to find height greater that 64 ft.
Answer (d):
$1\lt t \lt 4$

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