{"id":142,"date":"2018-01-16T11:50:11","date_gmt":"2018-01-16T03:50:11","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=142"},"modified":"2018-01-16T11:50:11","modified_gmt":"2018-01-16T03:50:11","slug":"up-and-down-motion-in-free-fall-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/up-and-down-motion-in-free-fall-problems-and-solutions.htm","title":{"rendered":"Up and down motion in free fall – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

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

1. A person throws a ball upward into the air with an initial velocity of 20 m\/s. Calculate how high it goes. Ignore air resistance. Acceleration due to gravity<\/a> (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

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

We use one of these 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 <\/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

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

We choose the upward direction as positive and downward direction as negative.<\/i><\/span><\/span><\/p>\n

Initial velocity (v<\/span><\/span>o<\/span><\/sub>)<\/span><\/span> = 20 m\/s (positive upward)<\/span><\/span><\/p>\n

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

Final velocity (v<\/span><\/span>t<\/span><\/sub>) <\/span><\/span>= 0 (it’s speed is zero for an instant at highest point)<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Maximum height (h) <\/span><\/span><\/p>\n

Solution :<\/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

0 = (20<\/span><\/span>2<\/span><\/span><\/sup>) + 2(-10) h<\/span><\/span><\/p>\n

0 = 400 – 20 h<\/span><\/span><\/p>\n

400 = 20 h<\/span><\/span><\/p>\n

h = 400 \/ 20 = 40 \/ 2 = 20 meters<\/span><\/span><\/p>\n

<\/p>\n

2. A person throws a stone upward at 20 m\/s while standing on the edge of a cliff, so that the stone can fall to the base of the cliff 100 meters below. <\/span><\/span><\/p>\n

(a) How long does it take the ball to reach the base of the cliff (b) Final velocity just before stone strikes the ground. Acceleration due to gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>. Ignore air resistance.<\/span><\/span><\/p>\n

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

We choose the upward direction as positive and downward direction as negative.<\/i><\/span><\/span><\/p>\n

High (h) = -100 meters (negative because final position below initial position)<\/span><\/span><\/p>\n

Initial velocity<\/a> (v<\/span><\/span>o<\/span><\/sub>) <\/span><\/span>= 20 m\/s (positive upward)<\/span><\/span><\/p>\n

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

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

(a) Time in air or time interval (t)<\/span><\/span><\/p>\n

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

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

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

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

High (h) = -100 meters (negative because final position below initial position)<\/span><\/span><\/p>\n

Initial velocity (v<\/span><\/span>o<\/span><\/sub>) <\/span><\/span>= 20 m\/s (positive upward), Acceleration of gravity (g) = -10 m\/s<\/span><\/span>2<\/span><\/span><\/sup> (negative downward).<\/span><\/span><\/p>\n

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

-100 = (20) t + \u00bd (-10) t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

-100 = 20 t – 5 t<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

-5 t<\/span><\/span>2<\/span><\/span><\/sup> + 20 t + 100 = 0<\/span><\/span><\/p>\n

We use quadratic formula :<\/span><\/span><\/p>\n

\"Up<\/p>\n

(b) Final velocity<\/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><\/sub>2<\/span><\/span><\/sup> = (20<\/span><\/span>2<\/span><\/span><\/sup>) + 2 (-10)(-100)<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = 400 + 2000<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub>2<\/span><\/span><\/sup> = 2400<\/span><\/span><\/p>\n

v<\/span><\/span>t<\/span><\/sub> = 49 m\/s<\/span><\/span><\/p>\n\n

[wpdm_package id=’515′]<\/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 – Up and down motion in free fall 1. A person throws a ball upward into the air with an initial velocity of 20 m\/s. Calculate how high it goes. Ignore air resistance. Acceleration due to gravity (g) = 10 m\/s2. Solution We use one of these kinematic equations for … 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":"Up and 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-142","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\/142","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=142"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/142\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}