Question

Will give brainiest. A ball is thrown from an initial height of 3 meters with an initial upward velocity of 20/ms . The ball's height h (in meters) after t seconds is given by the following. h=3+20t-5t^2 Find all values of t for which the ball's height is 8 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

Answer 1

We can complete the square to rewrite $h(t)$ as

$3+20t-5t^2=23-5(t-2)^2$

Then solve for when $h(t)=8$:

$23-5(t-2)^2=8\implies15=5(t-2)^2$

$\implies(t-2)^2=3$

$\implies t-2=\pm\sqrt3$

$\implies t=2\pm\sqrt3$

$\implies t\approx0.27\text{ or }t\approx3.73$