SOLUTION: Hello tutors! Here's my question: A rock is thrown. The height of the rock is h=-16t^2+54t+7 at any time, t, measured in seconds. The height is measured in feet. What was the ve

Algebra ->  Functions -> SOLUTION: Hello tutors! Here's my question: A rock is thrown. The height of the rock is h=-16t^2+54t+7 at any time, t, measured in seconds. The height is measured in feet. What was the ve      Log On


   

Question 1107305: Hello tutors!
Here's my question:
A rock is thrown. The height of the rock is h=-16t^2+54t+7 at any time, t, measured in seconds. The height is measured in feet.
What was the vertical distance the rock traveled?
Thank you to anyone that can help!
Amelia Brown
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the parabola is in the form:
+h%28t%29+=+a%2At%5E2+%2B+b%2At+%2B+c+ , and also when
+a+ is negative, as in this case, the formula
for the t-value of the maximum height is:
+t%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+54+
+t%5Bmax%5D+=+-54%2F%28+2%2A%28-16%29%29+
+t%5Bmax%5D+=+27%2F16+
Plug this value for t into the equation
and find +h%5Bmax%5D+
-----------------------
Here is the plot:
+graph%28+400%2C400%2C+-1%2C+5%2C+-10%2C+60%2C+-16x%5E2+%2B+54x+%2B+7+%29+



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Amelia,

look into my 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

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.