please help!!!!!!!!!!!!!!!!!11

Question

A ball is thrown from an initial height of 3

 feet with an initial upward velocity of 29ft/s

. The ball's height h

 (in feet) after t

 seconds is given by the following.

h=3 + 29t - 16t²

Find all values of t

 for which the ball's height is 15

 plefeet.

Answer 1

h= 3 +29t -16t^2

h(0) = 3 feet

v = h' = 29 -32t

v(0) = 29ft/s

h = 15 Solve 15 = 3 +29t -16t^2

16t^2 -29t -12 =0

t = 2.16 sec or t = 0.35 sec

t = (29 +/- sqrt(29^2 + 768)/32

t = 2.16 sec or t = 0.35 sec

Answer 2

You want to know when does h = 15.

This is found by solving the following equation:

-16t²+29t+3=15

That is a quadratic equation with a linear term (29t) so to solve, set equal to zero and use one of these techniques:

1) factoring

2) complete the square

3) quadratic formula

16t²-29t+12 = 0 (note, I visualized moving all terms to the right side of the equal sign so that the leading coefficient is positive--easier to factor).

However, this does not factor, so use the quadratic formula:

The following graph shows the answers as x₁ and x_2.

_{Try it yourself before using the graph to check.}

desmos.com/calculator/fky23dsxuc

Here is another graph that gives an alternate way to solve:

desmos.com/calculator/aqjqhjsoxp