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A trebuchet launches a projectile from a hilltop 30 feet above ground level on a parabolic arc at a velocity of 40 feet per second. The equation h = ?16t2 + 40t + 30 models the projectile's h height at t seconds. How long will it take for the projectile to hit its target on the ground? (to the nearest tenth of a second)

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altavistard

Answer:

t = 3.1 seconds

Step-by-step explanation:

Set the equation h = -16t^2 + 40t + 30 equal to 0 (0 represents ground level).

Then h = -16t^2 + 40t + 30 = 0

Applying the quadratic formula with a = -16, b = 40 and c = 30,

      -40 ± √( 1600 - 4[-16][30] )

t = -----------------------------------------

                  2(-16)

      -40 ± √ 3520

t = -------------------------

             -32

                                                                               -40 - 59.33

Only the positive t value makes sense.  It is t = ------------------

                                                                                      -32

t = 3.1 seconds

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