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-shir

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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-shir      Log On


   

Question 1028027: 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 the equation from #1 to find the initial velocity of the t-shirt.
What does the equation from #1 tell you about the value of the velocity, v, when t = 0?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-16t%5E2+%2B+v%2At+%2B+c+
Solve for +v+:
+v%2At+=++16t%5E2+-+c+%2B+h+
+v+=+16t+%2B+%28+h+-+c+%29+%2F+t+
----------------------
The initial height is when +t+=+0+
+h%280%29+=+-16%2A0%5E2+%2B+v%2A0+%2B+c+
+h%280%29+=+c+
given:
+c+=+5+ ft
+t+=+3+ sec
+h+=+131+
------------------
+v+=+16t+%2B+%28+h+-+c+%29+%2F+t+
+v+=+16%2A3+%2B+%28131+-+5+%29+%2F+3+
+v+=+48+%2B+126%2F3+
+v+=+48+%2B+42+
+v+=+90+ ft/sec
-------------------
+v+=+16t+%2B+%28+h+-+c+%29+%2F+t+
When +t+=+0+, then +h+=+c+ because
you are at the initial height
+%28+h-c+%29%2Ft+=+0%2F0+ and
+v+=+16%2A0+%2B+0%2F0+
+v+=+0%2F0+
That means you cannot determine the initial
velocity at +t+=+0+