I’ve finished reading your great questions on Preflight #6. I apologize it took me so long to process them, but I think you’ll find the discussion worth the wait! Below are anonymous responses from students, each of which is followed by my commentary.
“I keep getting confused on how the powers like feet/second squared eliminates”
That’s a great topic! The goal is to keep track of what is in the numerator and what is in the denominator. For example, when we calculate velocity as distance / time, we have meters in the numerator and seconds in the denominator. Thus, the units come out to m/s. If we take a velocity and multiply it by a time, we’ll have units of (m/s) * s. The first “s” is in the denominator. The second “s” is in the numerator. If you were rearrange it, you’d have (m*s) / s. Rearrange it a little more, and you’d have m * (s/s), and s/s = 1, so you’re left with meters.
Another way of thinking of it is in terms of negative exponents. Remember that dividing by a quantity is the same thing as multiplying by that quantity raised to the negative one power. So, our first example of calculating velocity as distance / time is equivalent to distance * (time-1). Thinking about the units, we have m * (s-1), which is the same thing as m/s. Our second example of calculating distance as velocity * time then has units of m * (s-1) * s. You can think of the “s” as s1, so that we have m * s-1 + 1 = m * s0 = m * 1 = m.
The negative exponent method also comes in handy when you think about the units for acceleration. Acceleration is defined as change in velocity divided by the change in time, which would have units of (m * s-1) / s, which, again, you can think of as (m * s-1) * (s-1). The units thus change into m * s-1 + -1 = m * s-2 which is the same thing as m / s2.
Ultimately, this is a skill that requires practice, so keep track of your units on every calculation you make (no matter how mundane), and you’ll have it down in no time!
“I only have a little bit of issues when I use Cos, Sin, and Tan to solve for problems.”
I think the most important thing to remember is the flow of information in the trig functions. The trig functions (sin, cos, tan) take in an angle and produce a number. That number is the ratio associated with that trig function (opp/hyp, adj/hyp, and opp/adj, respectively). Just remember that “sin(whatever)”, “cos(whatever)” and “tan(whatever)” are numbers, pure and simple. They’re just wearing a costume until you plug it into your calculator.
The inverse trig functions, on the other hand, take in a number and produce an angle. That number, again, is the ratio associated with that trig function.
“The only thing that I have trouble when it comes to any math is knowing when to use a formula. We learn a lot of formulas, and I can do them pretty good when were on the topic, but when we go back to it a while after i have trouble picking out which formula the question is asking for.”
Choosing an equation is a very important skill! I think that if you practice good bookkeeping at the beginning of the problem (writing down what you know and what you’re looking for), it can help the selection process.
I do notice you highlight that you have trouble remembering after “a while.” Might I suggest trying out problems immediately (or at least within a few hours) after class?
“It is taking multiple attempts for me to get [the problems] correct.”
That’s actually a very typical experience! Succeeding at physics requires practice—lots of it—which is why I think the Practice Flights are so valuable. Be sure to leave yourself enough time to try them again and again until you get the correct answer! (You might even need to plan to spend a few different sessions trying out the problems. For example, half an hour on Friday, Saturday, and Sunday each would be more valuable than 1.5 hours only on Sunday.)
