A ball is thrown from an initial height of 7 feet with an initial upward velocity of 33 ft/s. The ball’s height h (in feet) after t seconds is given by the following. h=7+33t-16t^2. Find all values of t for which the ball’s height is 23 feet.
Given that the height of the ball has been modeled by: h(t)=-16t^2+33t+7 the values of t for which h(t)=23 will be evaluated as follows: from our function, let h(t)=23 hence we shall have: 23=-16t^2+33t+7 re-writing the above we get: -16t^2+33t-16=0 solving the above using quadratic formula: t=[-b+/-sqrt(b^2-4ac)]/2a a=-16, b=33, c=-16 thus t=[-33+/-sqrt(33^2-4(-16)(-16))]/(-16*2) simplifying the above we get: t=33/32+/-sqrt(65)/32 hence t=1.2832 or 0.779
