.
Katie and Josh go mountain climbing. At one point Katie is on a ledge 6 meters directly above Josh.
Katie is thirsty so Josh tosses a water bottle straight up to Katie with an initial velocity of +14m/s.
The bottle rises and passes Katie on the way up, then it falls back down to her and she catches it as it falls.
A) at what time does the bottle pass Katie going up, and what time does she catch it
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Write the expression for the bottle's height
h(t) = -5t^2 + 14t.
Solve this equation for h(t) = 6
-5t^2 + 14t = 6
5t^2 - 14t + 6 = 0
= = .
= = 0.53 of a second is the time the bottle passes Katie first time moving up,
and
= = 2.27 seconds is the time the bottle passes Katie second time moving down.
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.