a) The times that the projectile will reach a height of 20.8 ft are 3.643 seconds and 0.357 seconds, respectively.
b) The projectile will hit the ground 4 seconds later of its launch.
<h3>How to analyze the launch of a projectile</h3>
Herein we find a physical model known as projectile motion, which considers that the motion of the object is created solely by gravity and effects from Earth's rotation and air viscosity are neglected. The height of the projectile is represented by the following quadratic equation:
s = - 16 · t² + 64 · t
In the first part, we need to determine when the projectile will reach a height of 20.8 feet:
20.8 = - 16 · t² + 64 · t
16 · t² - 64 · t + 20.8 = 0
(t - 3.643) · (t - 0.357) = 0
The times that the projectile will reach a height of 20.8 ft are 3.643 seconds and 0.357 seconds, respectively.
And the time when the projectile hits the ground is found by solving on t in the following quadratic equation:
- 16 · t² + 64 · t = 0
- 16 · t · (t + 4) = 0
The projectile will hit the ground 4 seconds later of its launch.
<h3>Remark</h3>
In the part (a) a dot symbol was omitted, correct part is: <em>Find the time(s) that the projectile will (a) reach a height of 20.8 ft. </em>
To learn more on quadratic equations: brainly.com/question/1863222
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