The time period the projectile at least 160 feet above the ground is 2 sec to 5sec.
What is time period?
The duration of time that a behavior lasts or a condition persists. Depending on the type of activity or situation under consideration, it may be measured in seconds or in millions of years.
Given function that represents height of the projectile above the ground is s feet is s = - 16t² + 112t.
To find the time period is the projectile at least 160 feet above the ground, make an inequality:
- 16t² + 112t ≥ 160
Subtract 160 from both sides:
- 16t² + 112t - 160 ≥ 0
Divide both sides by 16:
- t² + 7t - 10 ≥ 0
- t² + 2t + 5t - 10 ≥ 0
-t(t -2) + 5(t - 2) ≥ 0
(t - 2)( -t+ 5) ≥ 0
Either, t - 2 ≥ 0 → t ≥ 2
or, -t + 5 ≥ 0 → t ≤ 5
2 ≤ t ≤ 5
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