Okay so by the Pythagorean theorem, a^2 + b^2 = c^2
If we take the boy’s position at time t as a, then a = 5t, and the girl’s position b = t
Thus their distance at a given time is sqrt((5t)^2 + t^2) = sqrt(26t^2) =sqrt(26)t
Taking the derivative of that in terms of t gives us sqrt(26) feet
I think, it’s been like 10 years since I last studied calculus
I mean, precisely. It’s Pythagoras and linear algebra, this is not calculus.
Huh? You took the derivative by taking ‘t’ off the end, that ain’t calculus.
yeah ur right. but the rate of change of the distance between them is always sqrt(26) ft/s. the problem is flawed since it doenst actually require calculus to solve, just plug in t=1 and you get sqrt(26)
the problem is flawed
I hate questions that have this confusing language element (rate of separating… after 5 seconds) when it isn’t even clear if the person writing the question knew what they were asking. You’re left second-guessing the test-prompt, because now you’re double checking to see if the original 5 ft/s, 1 ft/s were actually accelerations rather than velocities. You’re worried that the answer is too easy, because it doesn’t involve the math you were prompted to study prior to the exam. You’re wasting time on parsing the language rather than doing the math.
Its just an awful way to conduct an exam, because its rewarding confidence rather than competence.
