{"id":43909,"date":"2025-06-30T10:58:15","date_gmt":"2025-06-30T10:58:15","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=43909"},"modified":"2025-06-30T10:58:28","modified_gmt":"2025-06-30T10:58:28","slug":"a-person-walks-20-meters-north-then-turns-30-degrees-east-of-norh-and-walks-another-15-meters","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-person-walks-20-meters-north-then-turns-30-degrees-east-of-norh-and-walks-another-15-meters\/","title":{"rendered":"A person walks 20 meters north, then turns 30 degrees east of norh and walks another 15 meters"},"content":{"rendered":"\n

A person walks 20 meters north, then turns 30 degrees east of norh and walks another 15 meters. Calculate the resultant displacement using trigonometric identities?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To calculate the resultant displacement, we can break the motion into its x (east-west) and y (north-south) components and then combine them.<\/p>\n\n\n\n

Step 1: Break the movement into components<\/h3>\n\n\n\n
    \n
  1. The person first walks 20 meters north. This motion is purely along the y-axis, so the x-component is 0 and the y-component is 20 meters.\n
      \n
    • x1=0x_1 = 0<\/li>\n\n\n\n
    • y1=20y_1 = 20<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • The person then turns 30\u00b0 east of north and walks 15 meters. This displacement has both x and y components.
      • To find the x and y components, we use trigonometric functions:
        • The x-component is 15\u22c5sin\u2061(30\u2218)15 \\cdot \\sin(30^\\circ).<\/li>
        • The y-component is 15\u22c5cos\u2061(30\u2218)15 \\cdot \\cos(30^\\circ).<\/li><\/ul><\/li><\/ul>Using known values:
          • sin\u2061(30\u2218)=0.5\\sin(30^\\circ) = 0.5<\/li>
          • cos\u2061(30\u2218)=32\u22480.866\\cos(30^\\circ) = \\frac{\\sqrt{3}}{2} \\approx 0.866<\/li><\/ul>So:\n
              \n
            • x2=15\u22c50.5=7.5x_2 = 15 \\cdot 0.5 = 7.5<\/li>\n\n\n\n
            • y2=15\u22c50.866\u224812.99y_2 = 15 \\cdot 0.866 \\approx 12.99<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

              Step 2: Add the components<\/h3>\n\n\n\n

              Now, combine the x and y components of both movements:<\/p>\n\n\n\n

                \n
              • Total x-component: xtotal=x1+x2=0+7.5=7.5x_{\\text{total}} = x_1 + x_2 = 0 + 7.5 = 7.5<\/li>\n\n\n\n
              • Total y-component: ytotal=y1+y2=20+12.99=32.99y_{\\text{total}} = y_1 + y_2 = 20 + 12.99 = 32.99<\/li>\n<\/ul>\n\n\n\n

                Step 3: Calculate the resultant displacement<\/h3>\n\n\n\n

                The resultant displacement RR is the vector sum of the total x and y components. We can find it using the Pythagorean theorem: R=xtotal2+ytotal2R = \\sqrt{x_{\\text{total}}^2 + y_{\\text{total}}^2}<\/p>\n\n\n\n

                Substitute the values: R=(7.5)2+(32.99)2\u224856.25+1084.60\u22481140.85\u224833.74 metersR = \\sqrt{(7.5)^2 + (32.99)^2} \\approx \\sqrt{56.25 + 1084.60} \\approx \\sqrt{1140.85} \\approx 33.74 \\text{ meters}<\/p>\n\n\n\n

                Step 4: Find the direction of the resultant displacement<\/h3>\n\n\n\n

                The direction (angle \u03b8\\theta) of the resultant displacement relative to north is given by: \u03b8=tan\u2061\u22121(xtotalytotal)\\theta = \\tan^{-1}\\left(\\frac{x_{\\text{total}}}{y_{\\text{total}}}\\right)<\/p>\n\n\n\n

                Substitute the values: \u03b8=tan\u2061\u22121(7.532.99)\u2248tan\u2061\u22121(0.227)\u224812.8\u2218\\theta = \\tan^{-1}\\left(\\frac{7.5}{32.99}\\right) \\approx \\tan^{-1}(0.227) \\approx 12.8^\\circ<\/p>\n\n\n\n

                So the resultant displacement is approximately 33.74 meters at an angle of 12.8\u00b0 east of north.<\/p>\n","protected":false},"excerpt":{"rendered":"

                A person walks 20 meters north, then turns 30 degrees east of norh and walks another 15 meters. Calculate the resultant displacement using trigonometric identities? The correct answer and explanation is: To calculate the resultant displacement, we can break the motion into its x (east-west) and y (north-south) components and then combine them. Step 1: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-43909","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43909","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=43909"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43909\/revisions"}],"predecessor-version":[{"id":43910,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43909\/revisions\/43910"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=43909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=43909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=43909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}