<|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.