Question 121033
Catapults fire projectiles that form a parabolic path. The height(h) in metres above the ground t seconds after the projectile leaves the catapult is given by the formula h=-4.9t^2 +4.2t+8.Use the quadratic formula to find the length of time the projectile is in the air before it hits the ground.
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That looks like a very slow projectile, anyway
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h = 0 when it strikes the ground so we have:
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-4.9t^2 + 4.2t + 8 = 0
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Use the quadratic formula: a=-4.9; b=4.2 c=8
{{{t = (-4.2 +- sqrt(4.2^2 - 4 * -4.9 * 8 ))/(2*-4.9) }}}
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{{{t = (-4.2 +- sqrt(17.4 - (-156.8) ))/(-9.8) }}}
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{{{t = (-4.2 +- sqrt(17.4 + 156.8 ))/(-9.8) }}}
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{{{t = (-4.2 +- sqrt(174.2 ))/(-9.8) }}}
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{{{t = (-4.2 - 13.1985)/(-9.8) }}}
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{{{t = (-173985)/(-9.8)}}}
t = 1.775 second