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use the quadratic formula to determine the times when an object launched vertically
from the surface of the earth at an initial speed of 40m/s reaches a height of 50 meters.
Include a sketch with the solution.
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The formula for the height under given conditions is
h(t) = -5t^2 + 40t.
The coefficient at t^2 is half of the gravity acceleration with the sign "minus".
The coefficient at "t" is the given initial vertical speed of 40 m/s.
To find the time, when the object will get the height of 50 m, you should solve
this equation
-5t^2 + 40t = 50,
or, which is equivalent,
t^2 - 8t + 10 = 0.
Usually, when a student obtains such a problem, it is assumed, that he (or she) just knows
the technique of solving quadratic equation using the quadratic formula
= = = = .
So, there are two solutions = = 1.55 seconds (rounded), which relates to ascending move,
and = = 6.45 seconds (rounded), which relates to the descending move.
The plot in (y,t)-coordinates is shown below.
Plot h(t) = -5t^2 + 40t (red) and h = 50 m (green)
Solved.
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At this site, there are lessons, where you can find many other similar solved problems
- 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.