Observing meteor from rocket
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Geschwindigkeit \(v\) /
The following formulas must be used to solve the exercise:
\(u' = \frac{u-v}{1-\frac{uv}{c^2}} \quad \)
No explanation / solution video to this exercise has yet been created.
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
An astronaut in a rocket traveling at .c with respect to Earth observes a meteor coming from behind and passing him at a speed he measures to be .c. How fast is the meteor moving with respect to earth?
Solution:
The speed of the meteor in his own mathcalS' frame is .c. The speed in the Earth frame mathcalS is therefore: u fracu'+v+fracvu'c^ frac.c+.c+frac.c .cc^ .c center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at .. mathcalS; scope scopescale. xshiftcm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillred!!white -- tooutin - tooutin tooutin --; %peak drawfillblue!!white -. tooutin . tooutin tooutin -.; %central flap drawfillblue!!white - tooutin - - tooutin -; %porthole drawcolorgrayultra thickfillwhite!!blue -. circle .cm; %fuel foreach i in ... pgfmathsetmacroxrand*. + *- - . pgfmathsetmacroyrand*. + *.-. pgfmathsetmacroopacValrand*.+ drawcolorred fillred!!yellow xy circle .cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at mathcalS'; drawcolorred thick stealth - -- noderight v.c; scope scopescale xshift-cm yshift.cm filldrawcolorblack fillblack circle .cm; drawcolorred thickstealth- .-.--.-. noderight u?; drawcolorblue thickstealth- ..--.. noderight u'.c; scope tikzpicture center
An astronaut in a rocket traveling at .c with respect to Earth observes a meteor coming from behind and passing him at a speed he measures to be .c. How fast is the meteor moving with respect to earth?
Solution:
The speed of the meteor in his own mathcalS' frame is .c. The speed in the Earth frame mathcalS is therefore: u fracu'+v+fracvu'c^ frac.c+.c+frac.c .cc^ .c center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at .. mathcalS; scope scopescale. xshiftcm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillred!!white -- tooutin - tooutin tooutin --; %peak drawfillblue!!white -. tooutin . tooutin tooutin -.; %central flap drawfillblue!!white - tooutin - - tooutin -; %porthole drawcolorgrayultra thickfillwhite!!blue -. circle .cm; %fuel foreach i in ... pgfmathsetmacroxrand*. + *- - . pgfmathsetmacroyrand*. + *.-. pgfmathsetmacroopacValrand*.+ drawcolorred fillred!!yellow xy circle .cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at mathcalS'; drawcolorred thick stealth - -- noderight v.c; scope scopescale xshift-cm yshift.cm filldrawcolorblack fillblack circle .cm; drawcolorred thickstealth- .-.--.-. noderight u?; drawcolorblue thickstealth- ..--.. noderight u'.c; scope tikzpicture center
Meta Information
Exercise:
An astronaut in a rocket traveling at .c with respect to Earth observes a meteor coming from behind and passing him at a speed he measures to be .c. How fast is the meteor moving with respect to earth?
Solution:
The speed of the meteor in his own mathcalS' frame is .c. The speed in the Earth frame mathcalS is therefore: u fracu'+v+fracvu'c^ frac.c+.c+frac.c .cc^ .c center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at .. mathcalS; scope scopescale. xshiftcm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillred!!white -- tooutin - tooutin tooutin --; %peak drawfillblue!!white -. tooutin . tooutin tooutin -.; %central flap drawfillblue!!white - tooutin - - tooutin -; %porthole drawcolorgrayultra thickfillwhite!!blue -. circle .cm; %fuel foreach i in ... pgfmathsetmacroxrand*. + *- - . pgfmathsetmacroyrand*. + *.-. pgfmathsetmacroopacValrand*.+ drawcolorred fillred!!yellow xy circle .cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at mathcalS'; drawcolorred thick stealth - -- noderight v.c; scope scopescale xshift-cm yshift.cm filldrawcolorblack fillblack circle .cm; drawcolorred thickstealth- .-.--.-. noderight u?; drawcolorblue thickstealth- ..--.. noderight u'.c; scope tikzpicture center
An astronaut in a rocket traveling at .c with respect to Earth observes a meteor coming from behind and passing him at a speed he measures to be .c. How fast is the meteor moving with respect to earth?
Solution:
The speed of the meteor in his own mathcalS' frame is .c. The speed in the Earth frame mathcalS is therefore: u fracu'+v+fracvu'c^ frac.c+.c+frac.c .cc^ .c center tikzpicturescale. scope%Earth filldrawcolorblue fillblue!!white circle cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at .. mathcalS; scope scopescale. xshiftcm yshiftcm %flaps coordinate P at --; drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scoperotate around:Pshift-cm-cmyscalexscal drawfillblue!!white - tooutin -. tooutin -. tooutin - -- -; scope %rocket drawfillred!!white -- tooutin - tooutin tooutin --; %peak drawfillblue!!white -. tooutin . tooutin tooutin -.; %central flap drawfillblue!!white - tooutin - - tooutin -; %porthole drawcolorgrayultra thickfillwhite!!blue -. circle .cm; %fuel foreach i in ... pgfmathsetmacroxrand*. + *- - . pgfmathsetmacroyrand*. + *.-. pgfmathsetmacroopacValrand*.+ drawcolorred fillred!!yellow xy circle .cm; drawcolorgreen!!black-latex --; drawcolorgreen!!black-latex --; nodecolorgreen!!black at mathcalS'; drawcolorred thick stealth - -- noderight v.c; scope scopescale xshift-cm yshift.cm filldrawcolorblack fillblack circle .cm; drawcolorred thickstealth- .-.--.-. noderight u?; drawcolorblue thickstealth- ..--.. noderight u'.c; scope tikzpicture center
Contained in these collections:
-
-
Geschwindigkeitstransformation by TeXercises