SOLUTION: The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 65 meters per second can be modeled by the parabola: f(x)=

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Question 184256: The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 65 meters per second can be modeled by the parabola: f(x)= x - 0.0023x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 65 meters per second can be modeled by the parabola: f(x)= x - 0.0023x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground.
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f(x)= x - 0.0023x^2
The highest point occurs when x = -b/2a = -1/(2*-0.0023) = 217.39 seconds
The height at that time is f(217.39) = 217.39 - 0.0023(217.39)^2
= 108.7 ft.
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Distance when it hits the ground?;
Distance will 2(217.39) = 434.78 feet
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You can get this result by solving
x - 0.0023x^2 = 0 since zero is the hight of the potato when it hits the ground.
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Cheers,
Stan H.