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If an object is propelled straight up weed from ground level with an initial velocity of 176 ft./s its height H in feet three seconds later is given by the equation H equals -16 T squared +1 7060 after how many seconds is a high 288 feet

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sqdancefan

Answer:

  the object is at 288 feet 2 seconds and 9 seconds after launch

Step-by-step explanation:

The equation of motion is given as ...

  h(t) = -16t² +176t

and we are asked to find when the object is at height 288 ft. Putting that number into the equation, we have ...

  288 = -16t² +176t

  -18 = t² -11t . . . . . . . . divide by -16

  -18 +30.25 = t² -11t +30.25 . . . . . . add (11/2)² to complete the square

  12.25 = (t -5.5)² . . . . . . simplify a bit

  ±3.5 = t -5.5 . . . . . . . . .square root

  t = 5.5 ± 3.5 = {2, 9}

The object is 288 feet high after 2 seconds or 9 seconds.

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