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For a water balloon launched from a 49-meter overlook with an initial vertical velocity of 24.5 meters per second,
the height h in meters as a function of time t in seconds is h=−4.9t^2+24.5t+49. When will the balloon land and burst?
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To answer the question, you should solve this equation
h(t) = 0, which is -4.9t^2 + 24.5t + 49 = 0.
Divide the left side by -4.9. You will get much more pleasant EQUIVALENT equation
t^2 - 5t - 100 = 0.
Use the quadratic formula to find its roots
= = .
Choose the positive root (and deny negative one)
t = = 12.81.
ANSWER. The event will happen in 12.81 seconds.
Solved and thoroughly explained.
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In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
- Introductory lesson 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.