SOLUTION: A projectile is fired from a cliff 1488 feet above the water at inclination of 45 degrees to the horizontal, with a velocity of 720 feet per second. The h of the projectile can be

Question 1099680: A projectile is fired from a cliff 1488 feet above the water at inclination of 45 degrees to the horizontal, with a velocity of 720 feet per second. The h of the projectile can be modeled by:
h(x)=-32x^2/720^2+x+1488
Where x is the horizontal distance of the projectile from the firing point

At what horizontal distance from the firing point will the projectile hit the ground? Feet:

I got the other parts to the question correct and finished. I cannot seem to get this last part to the problem correct. I have tried setting h(x) to zero but the answer never seems to come out right. Any help with would very appreciated, Thank you!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
set y = h(x) and you get:

y = -32x^2 / 720^2 + x + 1488

when you set y equal to 0, the formula becomes:

-32x^2 / 720^2 + x + 1488 = 0

this is a quadratic equation in standard form of ax^2 + bx + x = 0

therefore a = -32/720^2 and b = 1 and c =1488.

use the quadratic formula to solve this equation.

the formula states that:

x = (-b - sqrt(b^2 - 4ac)) / (2a)

or:

x = (-b + sqrt(b^2 - 4ac)) / (2a)

from there, it's a simple matter of replacing a,b,c with their respective values.

you will get:

x = (-1 - sqrt(1^2 - 4 * -32/720^2 * 1488)) / (2 * -32/720^2)

or:

x = (-1 + sqrt(1^2 - 4 * -32/720^2 * 1488)) / (2 * -32/720^2)

this becomes:

x = 17571.83192

or:

x = -1371.831924

if you have good graphing software, like the one found at https://www.desmos.com/calculator, then you can graph the equation of y = -32x^2 / 720^2 + x + 1488 and you will get what is shown below after adjusting the x and y limits correctly.

$$$

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