Question

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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

1. Solve the equation for initial velocity, v.
2. 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.
3. What does the equation from #1 tell you about the value of the velocity, v, when t = 0? Explain.

Answer 1

Explanation:

h = -16t^2 + vt + c

h + 16t^2 - c = vt

h + 16^2 - c

v = ---------------------

t

131 + 16(3)^2 - 5

v = ------------------------- = 90ft/s

3

The velocity is undefined when t=0. The equation is telling you it would take infinite velocity to travel some distance in zero time. The equation is meaningless in such a situation.

Answer 2

1.

`h=-16t^2+vt+c\qquad\text{original equation}\\\\h+16t^2-c=vt\qquad\text{subtract terms not containing v}\\\\v=(h+16t^2-c)/(t)\qquad\text{divide by the coefficient of v}`

2. Filling in the given numbers, we have ...

`v=(131+16(3)^2-5)/(3)=90\qquad\text{ft/s}`

3. The velocity is undefined when t=0. The equation is telling you it would take infinite velocity to travel some distance in zero time. The equation is meaningless in such a situation.