SOLUTION: At a basketball game, members of the Spirit Club use a t-shirt cannon to launch team t-shirts to spectators in the stands. The equation below describes the height, h, of the t-

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: At a basketball game, members of the Spirit Club use a t-shirt cannon to launch team t-shirts to spectators in the stands. The equation below describes the height, h, of the t-      Log On


   

Question 959302: At a basketball game, members of the Spirit Club use a t-shirt cannon to launch team t-shirts to spectators in the stands.
The equation below describes the height, h, of the t-shirt, t seconds after it is shot from the cannon c feet above the ground, at an initial velocity of v.
h = -16t^2 + vt + c
Solve the equation for initial velocity, v.
The cannon launched a t-shirt from an initial height of 5 feet.
After 3 seconds the shirt has reached a height of 131 feet.
Use your equation from #1 to find the initial velocity of the t-shirt.
Show your work.
What does the equation from #1 tell you about the value of the velocity, v, when t = 0? Explain.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-16t%5E2+%2B+v%2At+%2B+c+
-------------------------
change +h+ to +h%28t%29+
( helps to explain better )
+h%28t%29+=+-16t%5E2+%2B+v%2At+%2B+c+
----------------------------
The height is +5+ ft when the
cannon is fired at +t=0+, so
+h%280%29+=+5+
+5+=+-16%2A0%5E2+%2B+v%2A0+%2B+c+
+5+=+c+
-----------------------------
You are given:
+h%283%29+=+131+
+h%283%29+=+-16%2A3%5E2+%2B+v%2A3+%2B+5+
+131+=+-16%2A3%5E2+%2B+v%2A3+%2B+5+
+3v+=+131+%2B+16%2A9+-+5+
+3v+=+131+%2B+144+-+5+
+3v+=+275+-+5+
+3v+=+270+
+v+=+90+
The initial velocity is 90 ft/sec
----------------------------
When +t=0+
+h%280%29+=+-16%2A0%5E2+%2B+v%2A0+%2B+5+
+h%280%29+=+5+
What ever the velocity is at +t=0+
the height is still +5+ ft, so
the velocity can't be determined
from this equation