[BTW: My opinion is that this isn't pseudocontext for reasons I elaborate on in this comment.]
Calculus: Early Transcendental Functions. Larson Hostetler, Edwards. 2003. Houghton Mifflin.
Greg Hitt (a/k/a Sarcasymptote):
Et tu, Calculus?
Seriously, you are when I started to love math. Up until I met you, I trudged through year after year of pseudocontext, merely completing tasks only because they needed to be done and not out of some enjoyment or aching desire to do it. Then, you came along, and blew my freaking mind with your applicability. You were the math that worked.
And now look at you. Really, Calculus? Answer me this:
- What in the hell are you talking about? This is one of the most poorly worded questions I've ever seen. And is it common practice for someone to be so cavalier as to heave sandbags over the side from almost 200 feet in the air, all while carefully measuring both the height above the ground and the angle of elevation to the sun? I don't know, because I don't care about hot air balloons. I don't know anyone who does.
- Why are we worried about the rate of the movement of the shadow? Is the rate that a shadow moves across the ground useful for any situation? Is there some arbitrary race between the shadow of a sandbag and a log floating down a river? Seriously, related rates should be much more applicable than this.
- This is textbook, er… textbook. We could pretend to think about how to model the height, but instead, let's just skip the thinking and go right to a formula.
Moving Shadow. A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is 30° (see figure). Find the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters. [Hint: The position of the sandbag is given by s(t) = 60 - 4.9t2.]
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