sample_00008/raw_response.md

<|ref|>text<|/ref|><|det|>[[91, 80, 860, 107]]<|/det|>
The parametric equations for a projectile with constant gravity g: 

<|ref|>equation<|/ref|><|det|>[[152, 107, 426, 140]]<|/det|>
\[x = v_0 t \cos \theta + x_0\]

<|ref|>equation<|/ref|><|det|>[[152, 153, 565, 227]]<|/det|>
\[y = -\frac{1}{2} gt^2 + v_0 t \sin \theta + y_0\]

<|ref|>text<|/ref|><|det|>[[89, 255, 866, 308]]<|/det|>
ex. A shell is fired from ground level with an initial speed of 768 ft/sec. at an angle of 30°. Find: 

<|ref|>text<|/ref|><|det|>[[92, 309, 182, 351]]<|/det|>
1. \(\vec{r}(t)\) 

<|ref|>text<|/ref|><|det|>[[92, 357, 484, 380]]<|/det|>
2. the maximum altitude attained 

<|ref|>text<|/ref|><|det|>[[92, 383, 372, 407]]<|/det|>
3. the range of the shell 

<|ref|>text<|/ref|><|det|>[[92, 409, 360, 433]]<|/det|>
4. the speed on impact 

<|ref|>text<|/ref|><|det|>[[92, 436, 607, 460]]<|/det|>
5. the horizontal distance when \(y = 2240\) ft.