TeXercises.com

Projectile Motion

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.

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 -

Exercise

https://texercises.com/exercise/projectile-motion/

Question

Solution

Short

Video

\(\LaTeX\)

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!

Exercise:
The projectile motion of an object moving through air under the effect of gravitation and air resistance is given by the differential s * m ddot xt -beta vt v_xt m ddot yt -m g - beta vt v_yt where m is the mass of the object g the frefall acceleration beta a coefficient characterising the air resistance xt the horizontal position yt the vertical position v_xtdot xt the horizontal velocity component v_ytdot yt the vertical velocity component and vtsqrtv_x^t+v_y^t the speed of the object at time t. abcliste abc Decide if the system of differential s is linear or nonlinear and if it is timvariant or timinvariant. Give short reasons for your answers. hfill abc Write the differential s as a system of first-order differential s. hfill abcliste

Solution:
abcliste abc The system is non-linear because of the nonlinear term with vt. It is timinvariant because there is no explicit timdepency i.e. only the unknown functions xt yt v_xt and v_yt dep on the time. abc dot x v_x dot y v_y dot v_x -fracbetam sqrtv_x^+v_y^v_x dot v_y -g - fracbetam sqrtv_x^+v_y^v_y abcliste

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Systems of Differential Equations by by

3 | 7

Attributes & Decorations

Branches	Differential equations
Tags	non-linear, second-order, time-invariant
Content image
Difficulty	(1, default)
Points	4 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
Decoration
File
Link