SOLUTION: Not sure which category to put this Algebra question in: A golf ball is hit with an initial velocity of 150 feet per second at an inclination of 45 degrees to the horizontal. in

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Question 1098543: Not sure which category to put this Algebra question in:
A golf ball is hit with an initial velocity of 150 feet per second at an inclination of 45 degrees to the horizontal. in physics, it is established that the height h of the golf ball is given by the function:
h(x) = -32x^2/150^2 + x
Where X is the horizontal distance that the golf ball has traveled.
Use a graphing utility to determine the distance that the ball
has traveled when the height of the ball is 80 feet? (round to one decimal place) the answer is 92.1,611.1 ft. I just can't figure out how to figure this part out. How to find the answer.What to do to get the correct answer.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
they have essentially told you what the equation is that will solve this poblem for you.

what's left for you is to graph the equation and find out when the value of y is equal to 80.

the following graph does that.

you graph y = -32x^2/150^2 + x and you graph y = 80.

the intersection of those two equations is your solution.

my graph is shown below:

$$$

the graphing software i use is at https://www.desmos.com/calculator

their solution is rounded to three decimal points.

just round to 1 decimal point and you'll see that the solution is what you are looking for.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
They instruct you that your formula is

h(x) = -%28%2832%2Ax%5E2%29%2F150%5E2%29+%2B+x.


I forget about this "graphing utility" which is mentioned in the text, since I don't know what is they are talking about,
and, probably, I do not have it at all (thanks to god).


I will show you how to calculate it directly by hand.

Simply substitute the value of 80 into the formula and calculate:

h(x) = 80 = -%28%2832%2Ax%5E2%29%2F150%5E2%29+%2B+x.


Now you need to find x from this equation

80 = -%28%2832%2Ax%5E2%29%2F150%5E2%29+%2B+x.


For it, multiply both sides by 150^2 = 22500. You will get

80*22500 = -32x^2 + 22500x,   or,  equivalently,

32x^2 - 22500x  + 1800000 = 0.


Apply the quadratic formula

x%5B1%2C2%5D = %2822500+%2B-+sqrt+%2822500%5E2+-+4%2A32%2A1800000%29%29%2F%282%2A32%29 = %2822500+%2B-+16609%29%2F64.

x%5B1%5D = %2822500+-+16609%29%2F64 = 92;

x%5B2%5D = %2822500+%2B+16609%29%2F64 = 611.


Answer.  There are two solutions:  92 ft  and  611 ft  (approximately).




Plot y = -%28%2832%2Ax%5E2%29%2F150%5E2%29+%2B+x (red) and y = 80 (green)