Yup it's me ... Parametrics, who would have thought xD! Anyways, again ... I am doing review and I really need this grade to get an A in math class; that's why I am asking questions here. And you guys are wonderful enough to answer the test review questions. Have a test tomorrow, so I am getting prepared. Anyways, back to topic: this is the third-to-last question on test-review, and it says:
A dart is thrown from a point 5 feet above the ground with an inital velocity of 58 ft/sec and angle of elvation of $41 ^\circ$. Assume the onnly force acting on the dart is gravity. What is the maximum height reached by the dart? When and will the dart hit the ground? SHOW ALL WORK.
You know from my previous question that I don't understand what the question is even trying to say. So far, I did 20 questions out of 24 alone, and I need help on this. Please help me again, Math StackExchange Site!
Remember we are on Parametric Unit.
EDIT :
Equations(In my notes.. not sure if there are more.)
Examples
For a pre-calculus class you will probably have a set of parametric equations of the following form although your teacher might use different variables.
Given the initial position $(x(0),y(0))$, initial speed $\vert v \vert$ and initial direction of motion $\theta$ and acceleration $g$ due to gravity, then
\begin{equation} x(t)=x(0)+\vert v\vert t\cos\theta \end{equation}
\begin{equation} y(t)=y(0)+\vert v\vert t\sin\theta-\frac{g}{2}t^2 \end{equation}
For this exercise $x(0)=0,\,y(0)=5$ ft, $\vert v\vert=58$ ft/sec, $\theta=41^\circ$ and $g=32\text{ft/sec}^2$.
Substitute the values into the formula for $y(t)$ and you will get a second degree polynomial equation for $t$ (of the form $y=at^2+bt+c)$. Its graph will be a parabola which is concave downward and $y$ will achieve its greatest value at the vertex which occurs when $t=-\frac{b}{2a}$. Find that value of $t$ and substitute into the equation for $y$ to find out how high the dart goes.
The dart will hit the ground when $y(t)=0$ and $t>0$. So set the equation for $y(t)=0$ and solve for $t$ to find out when the dart will hit the ground. You only need to use $x(t)$ if you are asked how far the dart goes.