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Arlecino [84]
3 years ago
14

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms . The ball's height h (in meters) af

ter t seconds is given by the following. =h+2−9t5t2 Find all values of t for which the ball's height is 3 meters. Round your answer(s) to the nearest hundredth.
Mathematics
1 answer:
Alecsey [184]3 years ago
5 0

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms

Balls height h= 2 +9t -5t^2

To find all values of t for which the ball's height is 3 meters

We plug in 3 for h and solve for t

h= 2 +9t -5t^2

3 = 2 +9t -5t^2

Solve for t

0= -1+ 9t -5t^2

5t^2 - 9t + 1 = 0

Solve using quadratic formula

t= \frac{-b+- \sqrt{b^2-4ac} }{2a}

t= \frac{9+- \sqrt{(-9)^2-4*5*1} }{2*5}

After simplifying this,

t= \frac{9+\sqrt{61}}{10} = 0.11898

t= \frac{9-\sqrt{61}}{10} = 1.68102

the values of t for which the ball's height is 3 meters= 0.12 sec , 1.68 sec

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