{"id":140,"date":"2018-01-16T11:42:51","date_gmt":"2018-01-16T03:42:51","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=140"},"modified":"2018-01-16T11:42:51","modified_gmt":"2018-01-16T03:42:51","slug":"down-motion-in-free-fall-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/down-motion-in-free-fall-problems-and-solutions.htm","title":{"rendered":"Down motion in free fall – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Solved Problems in Linear Motion – Down motion in free fall<\/a><\/p>\n

1. A ball is thrown vertically downward with initial speed 10 m\/s and reach the ground in 2 seconds. Find final speed just before the ball hits the ground. Acceleration of gravity<\/a> (g) = 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>)<\/span><\/span> = 10 m\/s<\/span><\/span><\/p>\n

Time elapsed (t) = 2 seconds<\/span><\/span><\/p>\n

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

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

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

Acceleration 10 m\/s<\/span><\/span>2 <\/span><\/span><\/sup>means speed increase by <\/span><\/span>10 m\/s each second. After 3 second, speed = 30 m\/s. <\/span><\/span><\/p>\n

Final velocity = 10 m\/s + 20 m\/s = 30 m\/s.<\/span><\/span><\/p>\n

Kinematic equations for motion at constant acceleration<\/a>, as shown below :<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = v<\/span><\/span>o<\/span><\/sub> + a t \u2026……. 1<\/span><\/span><\/p>\n

h = v<\/span><\/span>o<\/span><\/sub> t + \u00bd a t<\/span><\/span>2 <\/span><\/span><\/sup>\u2026……. 2<\/span><\/span><\/p>\n

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

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

v<\/span><\/span>t<\/span><\/sub> = 10 + (10)(2) <\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = 10 + 20 = 30 m\/s<\/span><\/span><\/p>\n

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

2. A stone is thrown vertically downward from a bridge with initial speed 5 m\/s and reach the water in 2 seconds. Calculate the height of the bridge.<\/span><\/span><\/p>\n

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

Initial velocity (v<\/span><\/span>o<\/span><\/sub>)<\/span><\/span> = 5 m\/s<\/span><\/span><\/p>\n

Time elapsed (t) = 2 seconds<\/span><\/span><\/p>\n

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

Wanted :<\/u><\/span><\/span> the height of the bridge (h)<\/span><\/span><\/p>\n

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

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

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

h = 10 + (5)(4)<\/span><\/span><\/p>\n

h = 10 + 20<\/span><\/span><\/p>\n

h = 30 meters<\/span><\/span><\/p>\n\n

3. A ball is thrown vertically downward with initial speed 10 m\/s from a height of 80 meters. Find (a) Time in air (b) Final velocity just before ball strikes the ground.<\/span><\/span><\/p>\n

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

height (h) = 80 meters<\/span><\/span><\/p>\n

Initial velocity (v<\/span><\/span>o<\/span><\/sub>)<\/span><\/span> = 10 m\/s<\/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) Time interval (t)<\/span><\/span><\/p>\n

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

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

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

Final velocity :<\/u><\/span><\/span><\/p>\n

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

v<\/span><\/span>t<\/span><\/span><\/sub>2<\/span><\/span><\/sup> = (10)<\/span><\/span>2<\/span><\/span><\/sup> + 2(10)(80) = 100 + 1600 = 1700<\/span><\/span><\/p>\n

v<\/span><\/span>t <\/span><\/sub>= 41 m\/s<\/span><\/span><\/p>\n

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

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

41 = 10 + (10)(t)<\/span><\/span><\/p>\n

41 \u2013 10 = 10 t<\/span><\/span><\/p>\n

31 = 10 t<\/span><\/span><\/p>\n

t = 31 \/ 10 = 3,1 seconds<\/span><\/span><\/p>\n

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

v<\/span><\/span>t<\/sub> <\/span><\/span>= 41 m\/s<\/span><\/span><\/p>\n\n

[wpdm_package id=’513′]<\/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 – Down motion in free fall 1. A ball is thrown vertically downward with initial speed 10 m\/s and reach the ground in 2 seconds. Find final speed just before the ball hits the ground. Acceleration of gravity (g) = 10 m\/s2. Ignore air resistance. Known : Initial velocity (vo) … 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":"Down motion in free fall - 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-140","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\/140","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=140"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/140\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}