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Question
i need help with these problems, I have a crapy physics teacher :/
- Calculate the magnitude of the horizontal & vertical components of a vector that is 100 units long and is oriented at an angle of 45 degrees.
- the speed of falling rain is the same 10 m above ground as it is just before it hits the ground. what does this tell you about whether or not the rain encounters air resistance?

Answer
Hello Koraly,

1st -: I suspect that the 45 degrees is the measurement of the angle between the vector and vertical ... or maybe horizontal? Since the angle is 45 degrees it doesn't matter which, because the vector is 45 degrees from both horizontal and vertical. But if it hadn't been 45, you would have left me not knowing where the vector was pointing.

The steps to analyse this: Draw the vector inclined properly versus horizontal and vertical. From the bottom of the vector, draw a horizontal line under the vector. From the top of the vector, draw a vertical line down from the top. This should give you a triangle. You know one of the angles, and you know that the vertical and horizontal lines are perpendicular. Since the angles of a triangle have a total of 180 degrees, you can figure the 3rd angle. If the triangle is drawn to scale, the lengths of the horizontal and vertical sides of the triangle are the magnitude of the horizontal and vertical components of the vector.

If the vector you drew is 100 units long, and we give the name theta to the angle opposite the vertical side,
sin(theta) = the length of the vertical side / 100 units
After a bit of algebra, we have
the length of the vertical side = 100 units*sin(theta)
Since theta is 45 degrees in your problem,
the length of the vertical side = 70.7 units
And as I said above, that is the magnitude of the vertical component of the vector.

And you can easily say that
cos(theta) = the length of the horizontal side / 100 units
and
the length of the horizontal side = 70.7 units

Since I'm trying to teach you what your teacher hasn't, consider this. The angle between the vector and horizontal is 10 degrees. The horizontal component would be almost as long as the vector itself and the vertical component would be quite short -- right? If you're not sure, draw it and the triangle created by the steps I showed you above.

The magnitudes of the horizontal and vertical components will both be of the form
horizontal or vertical components = trig function(10 degrees)
The trig functions used for the horizontal or vertical components in cases like this are sine and cosine. What trig function would it be for the horizontal side? (Pretend you don't clearly remember the details I gave you above.) Sine of zero is zero and sine of 10 degrees is small (sine doesn't get to a value of 1.0 until the angle is 90 degrees). So it's cosine that would give you a magnitude almost as large as the original vector. When you understand how it works, you may find you don't need to make a drawing each time.

2nd -: Many falling things keep going faster as they continue to fall. That's because there is a downward force causing them to accelerate. That force is the object's weight. These drops of water don't accelerate because there is an upward force that cancels the downward force. With zero net force on the drop, the acceleration is zero, so the speed doesn't change. The most likely cause of the upward force is air resistance. (Or maybe there's a thirsty alien's spacecraft hovering above.)

I hope this helps,
Steve

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Steve Johnson

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I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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