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.

1. Draw a picture of the scenario
2. Identify all variables needed for the Kinematic Equations
3. Choose and write down the unmodified equation variation
4. Plug and chug for a solution
5. Verify that the solution is valid and sensible for the scenario

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.

1. What is the maximum height reached by the rocket?
2. How long after lift-off does the rocket reach its maximum height?
3. How long is the rocket in the air?

Draw shitty pictures in GIMP

Part 1 represents when the rocket is being launched into the air.

Part 2 represents when the rocket is slowing to its top of decent.

Part 3 represents the rocket falling back to earth.

• $V_i = 50.0 \text{ m/s}$
• $a = 2.00 \text{ m/s^2}$
• $D = 150 \text{ m}$
• $V_f = \text{ ?}$
• $t = \text{ ?}$

• $V_i = V_f$¹⁾
• $V_f = 0$
• $a = -9.8 \text{ m/s^2}$²⁾
• $D = \text{ ?}$
• $t = \text{ ?}$

• $D = 150 + D$³⁾
• $a = -9.8 \text{ m/s^2}$
• $V_i = 0$
• $t = \text{ ?}$

1. $= D_1 + D_2$
2. $= t_2$
3. $= t_1 + t_2$

1. $V_f^2 = V_i^2 + 2aD$
2. $V_f = V_i + at$
3. $V_f^2 = V_i^2 + 2aD$ (Part 2)
4. $V_f = V_i + at$ (Part 2)
5. $D = V_it + \frac{1}{2}at^2$ (Part 3)

1. $V_f^2 = (50.0)^2 + 2(2.00)(150)$
2. $V_f^2 = 2500 + 600$
3. $V_f^2 = 3100$
4. $\sqrt{V_f^2} = \pm\sqrt{3100}$
5. $\boxed{V_f = 55.6 \text{ m/s}}$⁴⁾

1. $55.6 = 50.0 + 2.00t$
2. $5.6 = 2t$
3. $\boxed{t = 2.8 \text{ secs}}$

1. $0 = (55.6)^2 + 2(-9.8)D$
2. $0 = 3091.36 + -19.6D$
3. $-3091.36 = -19.6D$
4. $\boxed{D = 157.7 \text{ m}}$

1. $0 = 55.6 + -9.8t$
2. $-55.6 = -9.8t$
3. $\boxed{t = 5.7 \text{ secs}}$

1. $307.7 = 0t + \frac{1}{2}(9.8)t^2$⁵⁾
2. $307.7 = 4.9t$
3. $\boxed{t = 7.9 \text { secs}}$

1. $\boxed{307.7 \text{ m}} = D$⁶⁾ $\checkmark$
2. $\boxed{8.5 \text{ secs}} = t + t$⁷⁾ $\checkmark$
3. $\boxed{16.4 \text{ secs}} = 8.5 + t$⁸⁾ $\checkmark$