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| + | ====== Five Steps ====== | ||
| + | According to Physics legend Mr. Brian Fudacz, Physics is __not__ math class and should be treated with high intellectual esteem. I don't really give a fuck but if we don't do these five steps we get points docked off on tests. | ||
| + | ===== Steps ===== | ||
| + | - Draw a picture of the scenario | ||
| + | - Identify all variables needed for the [[physics: | ||
| + | - Choose and write down the __unmodified__ equation variation | ||
| + | - Plug and chug for a solution | ||
| + | - Verify that the solution is valid and sensible for the scenario | ||
| + | |||
| + | ===== Example ===== | ||
| + | > A model rocket is launched straight upward with an initial speed of **50.0 m/s**. It accelerates with a constant upward acceleration of **2.00 m/s^2** until its engines stop at an altitude of **150 m**. | ||
| + | |||
| + | - What is the maximum height reached by the rocket? | ||
| + | - How long after lift-off does the rocket reach its maximum height? | ||
| + | - How long is the rocket in the air? | ||
| + | |||
| + | |||
| + | ==== Step 1 ==== | ||
| + | FIXME Draw shitty pictures in GIMP | ||
| + | === Part 1 === | ||
| + | Part 1 represents when the rocket is being launched into the air. | ||
| + | |||
| + | === Part 2 === | ||
| + | Part 2 represents when the rocket is slowing to its top of decent. | ||
| + | |||
| + | === Part 3 === | ||
| + | Part 3 represents the rocket falling back to earth. | ||
| + | |||
| + | ==== Step 2 ==== | ||
| + | === Variables === | ||
| + | == Part 1 == | ||
| + | * $V_i = 50.0 \text{ m/s}$ | ||
| + | * $a = 2.00 \text{ m/s^2}$ | ||
| + | * $D = 150 \text{ m}$ | ||
| + | * $V_f = \text{ ?}$ | ||
| + | * $t = \text{ ?}$ | ||
| + | |||
| + | == Part 2 == | ||
| + | * $V_i = V_f$((part 1's answer)) | ||
| + | * $V_f = 0$ | ||
| + | * $a = -9.8 \text{ m/ | ||
| + | * $D = \text{ ?}$ | ||
| + | * $t = \text{ ?}$ | ||
| + | |||
| + | == Part 3 == | ||
| + | * $D = 150 + D$((part 2's answer)) | ||
| + | * $a = -9.8 \text{ m/s^2}$ | ||
| + | * $V_i = 0$ | ||
| + | * $t = \text{ ?}$ | ||
| + | |||
| + | === Answers === | ||
| + | - $= D_1 + D_2$ | ||
| + | - $= t_2$ | ||
| + | - $= t_1 + t_2$ | ||
| + | |||
| + | ==== Step 3 ==== | ||
| + | === Equations === | ||
| + | - $V_f^2 = V_i^2 + 2aD$ | ||
| + | - $V_f = V_i + at$ | ||
| + | - $V_f^2 = V_i^2 + 2aD$ (Part 2) | ||
| + | - $V_f = V_i + at$ (Part 2) | ||
| + | - $D = V_it + \frac{1}{2}at^2$ (Part 3) | ||
| + | |||
| + | ==== Step 4 ==== | ||
| + | === Equation 1 === | ||
| + | - $V_f^2 = (50.0)^2 + 2(2.00)(150)$ | ||
| + | - $V_f^2 = 2500 + 600$ | ||
| + | - $V_f^2 = 3100$ | ||
| + | - $\sqrt{V_f^2} = \pm\sqrt{3100}$ | ||
| + | - $\boxed{V_f = 55.6 \text{ m/ | ||
| + | |||
| + | === Equation 2 === | ||
| + | - $55.6 = 50.0 + 2.00t$ | ||
| + | - $5.6 = 2t$ | ||
| + | - $\boxed{t = 2.8 \text{ secs}}$ | ||
| + | |||
| + | === Equation 3 === | ||
| + | - $0 = (55.6)^2 + 2(-9.8)D$ | ||
| + | - $0 = 3091.36 + -19.6D$ | ||
| + | - $-3091.36 = -19.6D$ | ||
| + | - $\boxed{D = 157.7 \text{ m}}$ | ||
| + | |||
| + | === Equation 4 === | ||
| + | - $0 = 55.6 + -9.8t$ | ||
| + | - $-55.6 = -9.8t$ | ||
| + | - $\boxed{t = 5.7 \text{ secs}}$ | ||
| + | |||
| + | === Equation 5 === | ||
| + | - $307.7 = 0t + \frac{1}{2}(9.8)t^2$((gravity isn't negative here; in the context of the problem, negative time wouldn' | ||
| + | - $307.7 = 4.9t$ | ||
| + | - $\boxed{t = 7.9 \text { secs}}$ | ||
| + | |||
| + | ==== Step 5 ==== | ||
| + | - $\boxed{307.7 \text{ m}} = D$((part 3's D value)) $\checkmark$ | ||
| + | - $\boxed{8.5 \text{ secs}} = t + t$((sum of the times of part 1 and 2)) $\checkmark$ | ||
| + | - $\boxed{16.4 \text{ secs}} = 8.5 + t$((part 3's answer)) $\checkmark$ | ||
