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Quadratic Word Problems: Projectile Motion
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A ball is thrown into the air with an upward velocity of 12 ft/sec. The
equation for the ball’s height (h) at any time (t) is h(t) = -4t^2 + 12t + 5.
(a) Find the maximum height attained by the ball.
(b) Find the time at which the ball reaches the ground.
(c) Find the time(s) at which the ball reaches a height of 10 ft.
___________________________________________________________________________
Disclaimer: To be technically correct in terms of a ball being thrown on Earth, the coefficient for the t^2-term in the equation for h(t) would have to be -16 (due to Earth's gravity). I chose the number -4 instead to keep the numbers/calculations small, since the focus of the video is more so on working with quadratic equations than modeling real-life projectile motion. For the equation I use in this problem, I am assuming that the ball is being thrown from a height of 5 feet and that the ball is under a gravitational influence of 8 ft/s^2 (Earth's gravity is 32 ft/s^2, but that's not the focus of the problem).
equation for the ball’s height (h) at any time (t) is h(t) = -4t^2 + 12t + 5.
(a) Find the maximum height attained by the ball.
(b) Find the time at which the ball reaches the ground.
(c) Find the time(s) at which the ball reaches a height of 10 ft.
___________________________________________________________________________
Disclaimer: To be technically correct in terms of a ball being thrown on Earth, the coefficient for the t^2-term in the equation for h(t) would have to be -16 (due to Earth's gravity). I chose the number -4 instead to keep the numbers/calculations small, since the focus of the video is more so on working with quadratic equations than modeling real-life projectile motion. For the equation I use in this problem, I am assuming that the ball is being thrown from a height of 5 feet and that the ball is under a gravitational influence of 8 ft/s^2 (Earth's gravity is 32 ft/s^2, but that's not the focus of the problem).
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