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Starts in Physics

Perhaps the most common question I am asked in physics is "how do I start this problem?"

I often use the following 6-step process for solving most physics problems:


1. Determine your starting location and positive direction (look at example for clarification).
2. Write down what you know. This includes any numbers given, their corresponding units, and the corresponding general variables (i.e. V for velocity, D for distance, etc.).
3. Use logic to determine any additional information that you know. For example, if there is a problem that dropping or shooting anything, chances are gravitational acceleration will be involved.
4. Look at all of the variables you have and determine what physics equation(s) that relate the information together with your end goal (what the question is asking for).
5. Solve it down to find the unknown.
6. Use logic to look at your answer and then be sure to use significant digits.

For example, say that I am trying to find the maximum height (from the lower ground) of a ball that is tossed upwards at a speed of 10.0 m/s on a cliff that is 30.0 m off the ground.


STEP 1:
I am standing on a cliff, so I have two options for my starting location: where I am standing or the base of the cliff. Since for me it is easier to put myself at zero, that is what I am declaring as my starting location. And, since I like to be "normal", the positive direction is upwards.

(Please note, I could have changed either of those assumptions without changing the answer to the problem. Different assumptions simply lead to different methods to solve the problem.)

STEP 2:
Initial Velocity: Vi = 10.0 m/s
Height (for later): D = 30.0 m (remember that my defined location is where I am standing, so this will not come into play yet)

STEP 3:
Acceleration of Gravity: A = -9.81 m/s^2 (remember that I defined up as being positive; since gravity pulls down, it is then a negative)

Also, using logic, I can figure out the final velocity of the ball at the maximum height. Since this is a 1-dimensional problem (only up/down), I can deduce that at the instant the ball is at the maximum height is when its velocity is zero. This is because at the instant of maximum height, the ball is not moving up nor down. So:

Final Velocity: Vf = 0 m/s
STEP 4:
I have Vi, A, Vf, and I am trying to find D, the distance the ball traveled upwards. I know that one physics formula is
Vf^2 = Vi^2 + 2*A*D
STEP 5:
(0)^2 = (10.0)^2 + 2(-9.81)(D)
0 = 100 -19.62 * D
-100 = -19.62*D
5.09684 = D
Sig Figs: D = 5.10 m

STEP 6:
Okay... so the ball's max height was 5.10m? Not exactly. When doing a problem, be sure to remember what you did in step 1: the assumptions we make about our starting location/direction. The problem is asking for the max height compared to the cliff base, but my start was at my own location. Thus, in order to answer the question, I need to add the 30.0m of the cliff to the 5.10m height of the ball to my position, giving me the final answer of 35.1 m for my maximum height.