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## Homework Statement

A stone is thrown upward from ground level. The initial speed is 32 ft/sec

a) In how many seconds will the stone hit the ground?

b) How high will it go?

c) With what minimum speed should the stone be thrown so as to reach a height of 36 ft?

## Homework Equations

y(t) = -16(t)

^{2 }+ v

_{0}(t) + y

_{0}

## The Attempt at a Solution

A) y(t) = -16(t)

^{2}+ 32(t) +0

0 = -16(t)

^{2}+32

t =

**2 sec till it hits the ground**

B)y'(t) = v(t) = -32t + 32

0 = -32t +32

t = 1 sec to reach max

-16 +32 =

**16 ft max**

C) y(t) = 36 ft y(t) = -16(t)

^{2}+32(t)

-16(t)

^{2}+32(t) = 36

+16(t)

^{2}-32(t) +36 = 0

4(4(t)

^{2 }- 8(t) + 9 = 0

Then I assumed I was doing it wrong : /

I continued onward to get (t-1)

^{2}= -(5/4)

t = 41/16

v(41/16) = -32(41/16) +32 = -50 =

**50 ft/s**

I got part c wrong naturally, any help on where it went wrong would be appreciated. Or if I did the first two wrong and just got the right answer. Either way, thanks for your time.

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