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MathNet 2010 — Part 06 Question 57

Math Olympiad Vault · MathNet 2010 — Part 06

Question 57

In a football match, the goalkeeper kicks the ball. The path of the ball is described with the function $$
h(x) = -0,0126 x^{2} + 0,635 x
$$, where the $h$ is the height of the ball above the ground and the $x$ is a horizontal distance from the place of impact (the quantities are expressed in measurement numbers). Question illustration
a) At what height is the ball when its horizontal distance from the impact site is $15~\mathrm{m}$?
b) How many meters from the impact site falls to Earth?
c) What is the maximum height the ball reaches? $$
h(x) = -0,0126 x^{2} + 0,635 x
$$ Question illustration