Question

while warming up at soccer practice, ellies teammate tosses the ball to ellie. ellie hits the ball upward with her head from a height of 1.6 meters at a velocity of 6 meters per second. the ball is in the air for some time until ellie catches it at a height of 1 meter. to the nearest tenth of a second, how long is the ball in the air before ellie catches it? hint: use the formula h = -4.9t² + vt + s.

Explanation:

Step1: Substitute values into formula

$1 = -4.9t^2 + 6t + 1.6$

Step2: Rearrange to quadratic equation

$-4.9t^2 + 6t + 0.6 = 0$

Step3: Apply quadratic formula $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$a=-4.9, b=6, c=0.6$
$t=\frac{-6\pm\sqrt{6^2-4(-4.9)(0.6)}}{2(-4.9)}$

Step4: Calculate discriminant

$\sqrt{36 + 11.76}=\sqrt{47.76}\approx6.91$

Step5: Solve for t (positive solution)

$t=\frac{-6-6.91}{-9.8}\approx1.3$

Answer:

1.3 seconds