Answer:
23.028 meters
Step-by-step explanation:
We presume your quadratic equation is intended to be ...
h(m) = -0.09m² +2m +1.67
where h(m) is the height in meters, and m is the horizontal distance in meters. You want to find the positive value of m when h = 0.
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The quadratic formula tells you the solution to ...
ax² +bx +c = 0
In your equation, a = -0.09, b = 2, c = 1.67, and the variable is m. The solutions given by the formula are ...
[tex]m=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-2\pm\sqrt{2^2-4(-0.09)(1.67)}}{2(-0.09)}\\\\=\dfrac{2\pm\sqrt{4+0.6012}}{0.18}\approx\{-0.806,23.028\}[/tex]
The shot landed about 23.028 meters from where it was thrown.
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Additional comment
The shot was launched at an angle of about 63.4° from the horizontal. Had a shallower angle been used with the same launch speed (about 16.5 m/s), the shot would have traveled farther. At about 45°, the distance might have been in excess of 29 meters.
