Question 88166: Can someone show me how to do this problem with step by step instructions. Thank you
The height h in feet of an object after t seconds is given by the function h=16t^2+90t+8.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Found 2 solutions by rapaljer, Earlsdon:
Answer by rapaljer(4671)   (Show Source):
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! The height of an object propelled upwards with an initial velocity of  from an initial height of  is given by:
 Notice that the coefficient of the first term is negative, due to the downward effect of gravity..
In your equation (corrected):
 The initial upward velocity is  and the initial height is 
To find out how long before the object hits the ground  set your equation = 0 and solve for the time, t.
Because the equation is a quadratic, you will, of course, get two answers for t.
One will be for when the object would have started from the ground (h=0), but because the initial height is 90 feet and not zero feet, this answer will be negative. The other answer will be the one you want because it will show the time that the object reaches the ground after rising then falling.
 You can use the quadratic formula to solve for t.  and in this problem, a = -16, b = 90, and c = 8.
Making the appropriate substitutions, we get:
 Simplifying this:
 Evaluating this:
 or  Discard the negative solution.
Answer is: t = 5.713 seconds.
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