Practice · Unlimited problems

Practice Lab

Fresh problems on everything in the module, as many as you like. Each one comes with hints and a worked solution built from its own numbers, and once you have solved it you can see it drawn to scale.

Practice problems

Choose a topic, or Mixed for a bit of everything. Type your answer and press Check (or Enter). Stuck? Take a hint, or open the worked solution, then try another problem of the same kind.

Topic

Streak 0 Best 0 Solved 0

Problem code …

Figure P.1 The current problem drawn to scale: the path, the particle, and its velocity (green) and acceleration (red) with their components. It stays hidden until you solve the problem or open its solution, so it never gives the answer away.

Load a problem by its code

Every problem has a code such as proj-40718, shown above the problem and in the page address. The same code always gives the same problem, so you can send one to a classmate or your instructor, or come back to it later.

Problem code

Your progress

Your streak counts problems solved on the first try, in a row. Hints are fine. A wrong answer, or opening the solution before you answer, starts the streak again.

Problems by topic. Rate = first-try solves as a share of problems tried.
Topic	Tried	First try	Solved	Rate

Typing answers

Answer boxes understand math, so you can type an expression instead of working out every decimal first. Each box shows how it read your input (for example = 17.72), so you can catch a typo before you check.

What you can type
You type	It reads
`sqrt(0.49.8180)`	\(\sqrt{313.92} \approx 17.72\)
`25^2/150`	\(625/150 \approx 4.167\)
`2sqrt(13)` or `2√13`	\(2\sqrt{13} \approx 7.211\)
`20cos(35°)`	\(20\cos 35^\circ \approx 16.38\)
`(1+0.1^2)^1.5*200`	\(203.0\)
`-3.048`	a decimal: accepted when it is within 1% of the exact value

Type only the number or expression; the unit is shown next to the box. Use \(g = 9.81\ \text{m/s}^2\). Answers are accepted within 1%, so three or four significant figures are plenty.