Question

EspañolA ball is thrown from an initial height of meters with an initial upward velocity of 9 m/s. The ball's heighth(in meters) after 1 seconds is given by the following.h=2 +91-512Find all values of t for which the ball's height is 3 meters.ARound your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)1 = secondsorХ5?initialheightground

Answer 1

We have

$h=2+9t-5t^2$

in order to know the time when h is equal to 3 we have

$3=2+9t-5t^2$

then

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

then we solve this equation using the general formula for second-degree equations

$t_{1,2}_{}=\frac{-9\pm\sqrt[]{9^2-4(-5)(-1)}}{2(-1)}$$t_{1,2}=\frac{-9\pm\sqrt[]{61}}{2(-5)}$

$t_1=0.118=0.12$$t_2=1.681=1.68$

We have two results when h=3, t1=0.12 seconds, and t2=1.68 seconds