PROJECTILE MOTIONS AND QUADRATIC FUNCTIONS
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Any object that is launched or thrown into the air is considered a projectile.
The general function for approximating the height h in feet after t seconds of a projectile on earth is given by \[h\left( t \right) = - \frac{1}{2}g{t^2} + {v_0}t + {h_0}\]. The different components \[g = {\rm{Acceleration due to gravity}}\;ft/{s^2}\] . \[{v_0} = {\rm{ Initial velocity in }}ft/s\]. \[{h_0} = {\rm{Initial height in feet}}\]. TIPS FOR SOLVING PROJECTILE MOTION EQUATIONS \[{\rm{Vertex of Projectile motion }}({t_{\max }},{h_{\max }})\] . \[{\rm{Maximum height = }}\,{h_{\max }} = h({t_{\max }}) = h\left( { - \frac{b}{{2a}}} \right)\] . \[{\rm{Time to reach max height = }}\,{t_{\max }} = - \frac{b}{{2a}}\] . \[{\rm{Time to reach hit the ground : solve }} - \frac{1}{2}g{t^2} + {v_0}t + {h_0} = 0\] . |
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EXAMPLE
A ball is thrown upward. The height h from the ground is given by the function \[h\left( t \right) = - 16{t^2} + 22t + 3\]
1.What is the initial velocity
2.What is the initial height before the ball is launched or released
3.What is the acceleration?
4.What is the maximum height?
5.When does the ball reach its maximum height?
6.When does the ball hit the ground?
A ball is thrown upward. The height h from the ground is given by the function \[h\left( t \right) = - 16{t^2} + 22t + 3\]
1.What is the initial velocity
2.What is the initial height before the ball is launched or released
3.What is the acceleration?
4.What is the maximum height?
5.When does the ball reach its maximum height?
6.When does the ball hit the ground?
Solution
