Question

Asanji stands at the edge of the top of a tall building and lobs a watermelon up into the air then proceeds to watch it fall to the street below (luckily it's empty because everybody is at home). The equation below represents the height, off the ground in meters, of the watermelon t seconds after Asanji has thrown it.
h = -4.9t^2 + 9.8t + 28

Approximately, how long does it take the watermelon to hit the ground? Round to the nearest tenth of a second.

Answer 1

9514 1404 393

Answer:

  3.6 s

Step-by-step explanation:

This is nicely solved by a graphing calculator. It takes about 3.6 seconds to hit the ground.

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We notice that the vertical velocity is a multiple of the leading coefficient, so we can solve this by completing the square.

  0 = -4.9(t^2 -2t) +28 . . . . . for h = 0

  28 +4.9 = 4.9(t^2 -2t +1) . . . . . rearrange, add 4.9 to both sides

  32.9/4.9 = (t -1)^2

  1 +(1/7)√329 = t ≈ 3.5912. . . . . square root and add 1

It takes about 3.6 seconds for the watermelon to hit the street.