====== 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:kinematic_equations|Kinematic Equations]]
  - 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))
  * $V_f = 0$
  * $a = -9.8 \text{ m/s^2}$((gravity))
  * $D = \text{ ?}$
  * $t = \text{ ?}$

== 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 ===
  - $V_f^2 = (50.0)^2 + 2(2.00)(150)$
  - $V_f^2 = 2500 + 600$
  - $V_f^2 = 3100$
  - $\sqrt{V_f^2} = \pm\sqrt{3100}$
  - $\boxed{V_f = 55.6 \text{ m/s}}$((negative is discarded as it doesn't make sense in context))

=== 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't make sense))
  - $307.7 = 4.9t$
  - $\boxed{t = 7.9 \text { secs}}$

==== 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)) $\checkmark$