SOLUTION: An object is fired straight up from the top of a 200-foot-tower at a velocity of 80 ft/s. Find the maximum height the object will reach. (Use the formula: S(t)=-16t^2+ vot+so where

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: An object is fired straight up from the top of a 200-foot-tower at a velocity of 80 ft/s. Find the maximum height the object will reach. (Use the formula: S(t)=-16t^2+ vot+so where      Log On


   

Question 1051151: An object is fired straight up from the top of a 200-foot-tower at a velocity of 80 ft/s. Find the maximum height the object will reach. (Use the formula: S(t)=-16t^2+ vot+so where vo is the initial velocity and so is the initial height.)
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+S%28t%29+=+-16t%5E2+%2B+80t++%2B+200+
+S%28t%29+=+-2t%5E2+%2B+10t+%2B+25+
Use the formula for the t-value
of the maximum height
+t%5Bmax%5D+=+-b%2F%282a%29+
+t%5Bmax%5D+=+-10%2F%282%2A%28-2%29%29+
t%5Bmax%5D+=+5%2F2+
-------------------
Plug this result back into formula to get +S%5Bmax%5D+
+S%5Bmax%5D+=+-16%2A%285%2F2%29%5E2+%2B+80%2A%285%2F2%29+%2B+200+
+S%5Bmax%5D+=+-16%2A%28+25%2F4+%29+%2B+200+%2B+200+
+S%5Bmax%5D+=+-100+%2B+400+
+S%5Bmax%5D+=+300+
The maximum height is 300 ft
------------------------------
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-30%2C+350%2C+-16x%5E2+%2B+80x+%2B+200+%29+

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
For more similar solved problems see the lessons
    - 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
in this site.

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".