Recent content by kuruman

A projectile's trajectory is optimized when there is only one value of the projection angle at which the quantity under consideration (e.g. horizontal range) is an extremum. In this article (see section "Projection angle optimization") it has been shown that the extremum projection angle is...

Ah, yes. That's what I missed.

I don't think so. ##2\times 1.013\times 10^5=202,600##. If you divide by 8.314, you don't get ##244,000## which is a larger number. when multiplied by the volume gives the right answer. Edited to fix problem with not considering the volume. See posts #5 and #6.

You are right and the answer is wrong. The average energy needs to be multiplied by Avogadro's number. "Typical" velocity is not typical use. It could mean r.m.s. velocity in the problem author's mind. Because the author of the solution apparently doesn't know the difference between the two or...

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An apparent paradox is that, if one assumes that the planet moves in a straight line at constant velocity, one gets the correct answer for part (a).

I messed up the definition of ##\sin\theta## because I copied and pasted from @brotherbobby's expression without changing ##s-x## to ##x## in the numerator. The original equation is inconsistent with the text. See edit note and added figure in post #4. Thanks for the catch.

Read about quarks here.

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Say I have vector ##\mathbf C## in a given 2D coordinate system specified by unit vectors ##\mathbf {\hat e}_1## and ##\mathbf {\hat e}_2.## In that system I write $$\mathbf C=C_1~\mathbf {\hat e}_1+C_2~\mathbf {\hat e}_2.$$In the above equation, ##C_1~\mathbf {\hat e}_1## and ##C_2~\mathbf...

I think your problem was that you measured the "jump in" distance from the starting point. If ##x_{opt}## is the optimum distance from C, the time will be a minimum no matter how far from C the man starts running as long as the starting point is at ##s>x_{opt}##. So it makes more sense to...

You don't have to repeat, I am with you 100%. I was expressing my doubts (in counterpoint to my "as it should be") about the respectability of NASA whose $125 million satellite to Mars crashed in 1999 because someone apparently used numbers without paying close attention to the units.

Yes it's interesting and as it should be. And then there is this (see below) from the people who landed people on the Moon almost 55 years ago. Resistance is futile.

It is reasonable and appropriate to say that. We say "a vector is the sum of its components". To translate this statement from English into mathematese, we write the equation$$\mathbf F=F_x~\mathbf {\hat x}+F_y~\mathbf {\hat y}.$$ However, when we ask "What is the x-component of vector...

If you are going to quote the Ampere-Maxwell law, quote it correctly. The displacement current term (Maxwell's correction) is ##\mathbf J_d=\dfrac{\partial \mathbf D}{\partial t}=\dfrac{\partial (\epsilon_0 \mathbf E)}{\partial t}##. The ##\epsilon_0## in the numerator cancels the one in the...