Question

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A ball is thrown from an initial height of 2 meters with an initial upward velocity of 11 m/s. The ball's height h (in meters) after t seconds is given by the following.

Answer 1

Answer:

Step-by-step explanation:

There will be 2 values of t for which the height is 7 because, first and foremost, this is a quadratic...a second degree polynomial.  Also, we know that when we throw something up, that it reaches a max height, then comes back down, passing on the way down all the things it passed on the way up.  The left side of your function is h(t), which represents the height of the object depending upon how long it's been in motion.  If we are asked to solve for t when the height is 7, we replace h(t) with 7 and solve the quadratic by factoring.  First, get everything on one side of the equation and set it equal to 0:

$7=-5t^2+11t+2$

becomes

$-5t^2+11t-5=0$

Factor that whichever way you are most familiar with (the quadratic formula will ALWAYS work for quadratics!) and get the values of t:

t = .64 seconds and

t = 1.56 seconds