Problem 44365. An asteroid and a spacecraft

Created by AMITAVA BISWAS

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;#128640 Imagine a non-relativistic simple situation.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Assume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Your spacecraft started from the position p0 at time t0.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Your spacecraft is moving with a constant velocity.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Your spacecraft is expected to reach a star at the location p1 at time t1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You just heard over the radio that an asteroid has been identified at the location p2 at time t0.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The asteroid is moving with a constant velocity.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The asteroid is expected to reach another star at the location p3 at time t1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

495 Solutions
157 Solvers

Last Solution submitted on Apr 16, 2023

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Stephen Cohen on 18 Oct 2017

Needs more test cases to eliminate the the trivial non-solution that exploits the lack of test cases.

Rafael S.T. Vieira on 8 Jul 2020

This problem needs more test cases. My solution probably is not general, but it works without using all of its tests.

Rafael S.T. Vieira on 8 Jul 2020

An interesting test case, for instance, would be (that my solution and many others would fail):

p0 = [1, 0, 0];
p1 = [ -1, 0, 0];
p2 = [ 0, 1, 0.5];
p3 = [ 0, -1, 0.5];
t0 = 0;
t1 = 1;
d = 1;
ok = false;

At half-way their path, asteroid and spacecraft will be at distance 0.5 of each other, violating the safe distance d=1, and without crossing paths.

Solution Comments

Show comments

Problem Recent Solvers157

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!