SOLUTION: A firework is launched upward at an initial velocity of 49 m/s, from a height
of 1.5 m above the ground. The height of the firework, in metres, after t seconds, is modelled by the
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Question 1187125: A firework is launched upward at an initial velocity of 49 m/s, from a height
of 1.5 m above the ground. The height of the firework, in metres, after t seconds, is modelled by the equation h=4.9t^2 + 49t + 1.5.
a) What is the maximum height of the firework above the ground?
b) Over what time interval is the height of the firework greater than 100 m above
the ground? Round to the nearest hundredth of a second.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I assume this should be h(t)=-4.9t^2+49t + 1.5
this is a negative quadratic so the vertex t=-b/2a is the time at maximum, and that is -49/-9.8 or 5 seconds
the maximum height is 124 m.
solve for -4.9t^2+49t+1.5=100
or-4.9t^2+49t-98.5=0=4.9t^2-49t+98.5
t=(1/9.8)(49+/-sqrt (2401-1930.6)); square root=21.69
t=70.69/9.8=7.24 sec
t=27.31/9.8=2.79 sec.
those are the times
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
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.
Start from the very first lesson, which explains HOW TO an equation should be written,
because in your post it is written incorrectly ( ! )
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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