{"id":138,"date":"2018-01-16T11:30:36","date_gmt":"2018-01-16T03:30:36","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=138"},"modified":"2018-01-16T11:30:36","modified_gmt":"2018-01-16T03:30:36","slug":"freely-falling-objects-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/freely-falling-objects-problems-and-solutions.htm","title":{"rendered":"Freely falling objects \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Solved Problems in Linear Motion – Freely falling objects<\/a><\/p>\n

1. An object dropped from the top of a cliff. It is seen to hit the ground below after 3 seconds. Determine its velocity just before hitting the ground. Acceleration of gravity<\/a> is 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>. Ignore air resistance.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Initial velocity (v<\/span><\/span>o<\/span><\/sub>) = 0 (object dropped)<\/span><\/span><\/p>\n

Time interval (t) <\/span><\/span>= 3 seconds<\/span><\/span><\/p>\n

Acceleration of gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted :<\/u><\/span><\/span> Final velocity (v<\/span><\/span>t<\/span><\/sub>)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Acceleration due to gravity at the surface of the earth, its magnitude is 9.8 m\/s<\/span><\/span>2<\/span><\/span><\/sup>. To make calculation easier, we use 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

10 m\/s<\/span><\/span>2<\/span><\/span><\/sup> or 10 m\/s \/ 1 second, means that the speed increases linearly in time by 10 m\/s during each second.<\/span><\/span><\/p>\n

After 1 second, object’s speed = 10 m\/s<\/span><\/span><\/p>\n

After 2 seconds, object’s speed = 20 m\/s<\/span><\/span><\/p>\n

After 3 seconds, object’s speed = 30 m\/s.<\/span><\/span><\/p>\n

We also can use kinematic equations for motion at a constant acceleration<\/a>, as shown below.<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = v<\/span><\/span>o<\/span><\/sub> + a t <\/span><\/span><\/p>\n

s = v<\/span><\/span>o<\/span><\/sub> t + \u00bd a t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = v<\/span><\/span>o<\/span><\/sub>2<\/span><\/span><\/sup> + 2 a s<\/span><\/span><\/p>\n

Free fall has no initial velocity (v<\/span><\/span>o<\/span><\/sub> = 0), so above equation can be changed as shown below :<\/span><\/span><\/p>\n

Equation of Free fall motion<\/a> :<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = g t \u2026……… 1<\/span><\/span><\/p>\n

h = \u00bd g t<\/span><\/span>2 <\/span><\/span><\/sup>\u2026……… 2<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = 2 g h \u2026……….. 3<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = g t<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = (10)(3) <\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = 30 m\/s<\/span><\/span><\/p>\n

Final velocity is 30 m\/s<\/span><\/span><\/p>\n\n

2. A body falls freely from rest, from a height of 25 m. Find (a) The speed with which it strikes the ground. (b) The time it takes to reach the ground.<\/span><\/span><\/p>\n

Acceleration due to gravity at the surface of Earth is 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Height (h) = 5 meters<\/span><\/span><\/p>\n

Acceleration of gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted :<\/u><\/span><\/span><\/p>\n

(a) Final velocity (vt<\/sub>)<\/span><\/span><\/p>\n

(b) Time interval (t)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Free fall’s equation :<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = g t<\/span><\/span><\/p>\n

h = \u00bd g t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = 2 g h<\/span><\/span><\/p>\n

(a) Final velocity (v<\/span><\/span>t<\/span><\/sub>)<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = 2 g h = 2(10)(5) = 100 <\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = 10 m\/s<\/span><\/span><\/p>\n

(b) Time interval (t)<\/span><\/span><\/p>\n

h = \u00bd g t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

5 = \u00bd (10) t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

5 = 5 t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

t<\/span><\/span>2<\/span><\/span><\/sup> = 5\/5 = 1<\/span><\/span><\/p>\n

t = 1 second<\/span><\/span><\/p>\n\n

3. A ball dropped from a height. Find (a) Acceleration (b) Distance after 3 seconds (c) Time in air if final velocity is 20 m\/s. Acceleration due to gravity = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Known <\/u><\/span><\/span>:<\/span><\/span><\/p>\n

Acceleration of gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted :<\/u><\/span><\/span><\/p>\n

(a) Acceleration (a)<\/span><\/span><\/p>\n

(b) Distance<\/a> or height (h) if time elapsed (t) = 3 seconds<\/span><\/span><\/p>\n

(c) Time interval (t) if v<\/span><\/span>t<\/span><\/sub> = 20 m\/s<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Free fall’s equation :<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = g t<\/span><\/span><\/p>\n

h = \u00bd g t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = 2 g h<\/span><\/span><\/p>\n

(a) Acceleration (a)<\/span><\/span><\/p>\n

Acceleration = acceleration due to gravity = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>. It means speed increase by 10 m\/s each second.<\/span><\/span><\/p>\n

(b) Distance or height (h) after t = 3 seconds<\/span><\/span><\/p>\n

h = \u00bd g t<\/span><\/span>2 <\/span><\/span><\/sup>= \u00bd (10)(3)<\/span><\/span>2<\/span><\/span><\/sup> = (5)(9) = 45 meters<\/span><\/span><\/p>\n

(c) Time elapsed (t) if v<\/span><\/span>t<\/span><\/sub> = 20 m\/s<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = g t<\/span><\/span><\/p>\n

20 = (10) t<\/span><\/span><\/p>\n

t = 20 \/ 10 = 2 seconds<\/span><\/span><\/p>\n

<\/p>\n

[wpdm_package id=’511′]<\/p>\n

[wpdm_package id=’517′]<\/p>\n

    \n
  1. Distance and displacement<\/a><\/li>\n
  2. Average speed and average velocity<\/a><\/li>\n
  3. Constant velocity<\/a><\/li>\n
  4. Constant acceleration<\/a><\/li>\n
  5. Free fall motion<\/a><\/li>\n
  6. Down motion in free fall<\/a><\/li>\n
  7. Up and down motion in free fall<\/a><\/li>\n<\/ol>\n

    <\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

    Solved Problems in Linear Motion – Freely falling objects 1. An object dropped from the top of a cliff. It is seen to hit the ground below after 3 seconds. Determine its velocity just before hitting the ground. Acceleration of gravity is 10 m\/s2. Ignore air resistance. Known : Initial velocity (vo) = 0 (object … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Freely falling objects \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-138","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=138"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/138\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}