# If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h = -16t^2 + vt + s (where h and s are in ft, t is in...

If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h = -16t^2 + vt + s (where h and s are in ft, t is in seconds and v is in ft/sec.)

If a rock is thrown upward from a height of 100 ft, with an initial velocity of 32 ft/sec, sholve for the itme that it takes for it to hit the ground (when h = 0).

Round your answer to 2 decimals.

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`h = -16t^2 + vt + s`

s = original position = 100ft

v = 32 ft/sec

h = 0 when it hits ground

Solve for t.

`0 = -16t^2 + 32t + 100`

`0 = (-32+-sqrt(32^2 - 4(-16)(100)))/(2(-16))`

`0 = (-32+-sqrt(7424))/-32`

`0 = -1.6925and 3.6925`

Since time is not negative, -1.6925 is an extraneous solution, therefore it takes **3.69 seconds for the object to hit the ground**.

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