{"id":480,"date":"2012-09-27T21:25:49","date_gmt":"2012-09-27T21:25:49","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=480"},"modified":"2012-09-27T21:31:01","modified_gmt":"2012-09-27T21:31:01","slug":"adding-vectors-the-chart-thing","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/adding-vectors-the-chart-thing\/","title":{"rendered":"Adding Vectors: The “chart thing”"},"content":{"rendered":"

Especially when tutoring physics 12, vector addition comes up.\u00a0 Let’s use the “chart thing”:<\/h2>\n

I took Physics 12 in 1988.\u00a0 In that class, we\u00a0added vectors component-wise.\u00a0 However, at university they used sine law and cosine law.\u00a0 I haven’t seen someone use component-wise addition in over twenty years – until this week.\u00a0 Now, they call it “the chart thing:)”<\/p>\n

Let’s\u00a0imagine we’re adding the following two vectors:\"vector\"vector<\/p>\n

Well, first we use trig to resolve each into horizontal (x) and vertical (y) components:<\/p>\n

\"vector\"vector<\/p>\n

Now, looking above, we see that for the first vector, the x component is pointing left:\u00a0 it’s negative.\u00a0 A downward component would be negative as well, but we don’t have any downward components in this problem.<\/p>\n

Now, to the chart:<\/p>\n\n\n\n\n\n\n
vector<\/strong><\/td>\nx component<\/strong><\/td>\ny component<\/strong><\/td>\n<\/tr>\n
vector 1<\/td>\n-12.3<\/td>\n8.60<\/td>\n<\/tr>\n
vector 2<\/td>\n12.0<\/td>\n18.5<\/td>\n<\/tr>\n
total: result vector<\/strong><\/td>\n-0.3<\/td>\n27.1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

You just add downwards to get the total x and y components of the resultant vector.\u00a0 We see that the result has -0.3 for its x component and 27.1 for its y component.\u00a0 We can build it as follows:<\/p>\n

\"resultant
\nNow, use a\u00b2 + b\u00b2 = c\u00b2 to get the hypotenuse. Of course, you’ll still get 27 (two sig digits), since 0.3 is too small to have any significant effect on the vertical component of 27.1. Use 2ndtan(27.1\/0.3) – you may also know it as arctan(27.1\/0.3) – to get the angle of 89\u00b0.
\n\"resultant<\/p>\n

Since there were only two significant digits in the original problem, we should give the answer with two.\u00a0 (This isn’t always true, technically, but it’s a good rule of thumb.)\u00a0 Hence, we give the answer in two sig digs: 27 m\/s 89\u00b0 N of W.<\/p>\n

Jack of Oracle Tutoring by Jack and Diane<\/a>, Campbell River, BC.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Especially when tutoring physics 12, vector addition comes up.\u00a0 Let’s use the “chart thing”: I took Physics 12 in 1988.\u00a0 In that class, we\u00a0added vectors component-wise.\u00a0 However, at university they used sine law and cosine law.\u00a0 I haven’t seen someone …<\/p>\n

Adding Vectors: The “chart thing”<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-480","post","type-post","status-publish","format-standard","hentry","category-physics"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/480","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=480"}],"version-history":[{"count":29,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/480\/revisions"}],"predecessor-version":[{"id":509,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/480\/revisions\/509"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=480"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=480"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=480"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}