{"id":278358,"date":"2025-08-02T04:10:04","date_gmt":"2025-08-02T04:10:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278358"},"modified":"2025-08-02T04:10:06","modified_gmt":"2025-08-02T04:10:06","slug":"assume-there-are-36-passenger-capsules-evenly-spaced-around-the-circumference","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/02\/assume-there-are-36-passenger-capsules-evenly-spaced-around-the-circumference\/","title":{"rendered":"Assume there are 36 passenger capsules, evenly spaced around the circumference."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Of course. Here is the solution to the Ferris wheel problem with a detailed explanation.<\/p>\n\n\n\n

Correct Answer<\/strong><\/h3>\n\n\n\n

The heights of the five unnumbered passenger capsules, starting from the lowest to the highest, are approximately:<\/p>\n\n\n\n

    \n
  • Capsule at 15\u00b0:<\/strong>\u00a015.53 meters<\/li>\n\n\n\n
  • Capsule at 30\u00b0:<\/strong>\u00a030.00 meters<\/li>\n\n\n\n
  • Capsule at 45\u00b0:<\/strong>\u00a042.43 meters<\/li>\n\n\n\n
  • Capsule at 60\u00b0:<\/strong>\u00a051.96 meters<\/li>\n\n\n\n
  • Capsule at 75\u00b0:<\/strong>\u00a057.95 meters<\/li>\n<\/ul>\n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    This problem requires the use of trigonometry to determine the vertical height of passenger capsules on a Ferris wheel. We can model the wheel on a coordinate plane, with its center at the origin (0,0). The height of each capsule above the ground corresponds to its y-coordinate.<\/p>\n\n\n\n

    First, we identify the key information. The radius of the Ferris wheel is 60 meters. In our trigonometric model, the radius acts as the hypotenuse of a right-angled triangle formed by a capsule’s position. The height we want to find is the side opposite the angle of rotation.<\/p>\n\n\n\n

    The relationship between the angle (\u03b8), the radius (hypotenuse), and the height (opposite side) is given by the sine function:
    sin(\u03b8) = Opposite \/ Hypotenuse
    Therefore, Height = Radius \u00d7 sin(\u03b8).<\/p>\n\n\n\n

    Next, we must determine the angle for each unnumbered capsule. The diagram shows the first quadrant of the wheel, a 90-degree arc, is divided into six equal sections by the spokes. To find the angle of each section, we divide the total angle by the number of sections:
    Angle per section = 90\u00b0 \/ 6 = 15\u00b0.<\/p>\n\n\n\n

    This means the passenger capsules are located at angles of 15\u00b0, 30\u00b0, 45\u00b0, 60\u00b0, and 75\u00b0 from the horizontal starting point.<\/p>\n\n\n\n

    Now, we can calculate the height for each capsule using the formula Height = 60 \u00d7 sin(\u03b8):<\/p>\n\n\n\n

      \n
    1. For the capsule at 15\u00b0:<\/strong>
      Height = 60 \u00d7 sin(15\u00b0) \u2248 60 \u00d7 0.2588 \u2248 15.53 meters.<\/li>\n\n\n\n
    2. For the capsule at 30\u00b0:<\/strong>
      Height = 60 \u00d7 sin(30\u00b0) = 60 \u00d7 0.5 = 30.00 meters.<\/li>\n\n\n\n
    3. For the capsule at 45\u00b0:<\/strong>
      Height = 60 \u00d7 sin(45\u00b0) \u2248 60 \u00d7 0.7071 \u2248 42.43 meters.<\/li>\n\n\n\n
    4. For the capsule at 60\u00b0:<\/strong>
      Height = 60 \u00d7 sin(60\u00b0) \u2248 60 \u00d7 0.8660 \u2248 51.96 meters.<\/li>\n\n\n\n
    5. For the capsule at 75\u00b0:<\/strong>
      Height = 60 \u00d7 sin(75\u00b0) \u2248 60 \u00d7 0.9659 \u2248 57.95 meters.<\/li>\n<\/ol>\n\n\n\n

      These calculations provide the vertical distance from the center of the wheel to each capsule, which represents its height from the ground.<\/p>\n\n\n\n

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

      The Correct Answer and Explanation is: Of course. Here is the solution to the Ferris wheel problem with a detailed explanation. Correct Answer The heights of the five unnumbered passenger capsules, starting from the lowest to the highest, are approximately: Explanation This problem requires the use of trigonometry to determine the vertical height of passenger […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-278358","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278358","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=278358"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278358\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}