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Question 1161808: Suppose that a bottle rocket is launched upward with a initial velocity of 96ft/sec from a height of 880ft. Its height is h, in feet, after t seconds is given by h(t)=-16tsquared + 96t + 880. After how long will the rocket reach the ground?
Answer by ikleyn(52797)   (Show Source):
You can put this solution on YOUR website! .
To find the flight time t, solve the equation
h(t) = 0,
which is
-16*t^2 + 96t + 880 = 0.
Factor it in two steps. First step is
-16*(t^2 - 6t - 55) = 0,
which is EQUIVALENT to
t^2 - 6t - 55 = 0.
Factor the last equation
(t-11)*(t+5) = 0.
Of the two roots, t= -5 and t= 11, only positive t= 11 is the solution to the problem.
ANSWER. The time to hit ground is 11 seconds.
Solved.
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In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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