Question

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 20 m/s. The ball's height h (in meters) after t seconds is given by h=2+20t-5t^2. find all values of t for which the ball's height is 12 meters. Round your answers to the nearest tenth of a second.

Answer 1

2+20t-5t^2=12

5t^2-20t+10=0

t^2-4t+2=0  complete the square

t^2-4t=-2

t^2-4t+4=2  

(t-2)^2=2

t-2=±$\sqrt{2}$

t=2±$\sqrt{2}$

t≈(0.586, 3.41)