{"id":2419,"date":"2018-05-05T06:40:44","date_gmt":"2018-05-04T22:40:44","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=2419"},"modified":"2023-08-06T15:17:46","modified_gmt":"2023-08-06T15:17:46","slug":"vertical-motion-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/vertical-motion-problems-and-solutions.htm","title":{"rendered":"Vertical motion \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Vertical motion \u2013 problems and solutions<\/span><\/p>\n

1. Ball A threw vertically upward with the speed<\/a> of 10 m\/s. 1 second later, from the same position, Ball B is thrown vertically upward at the same path, with the speed of 25 m\/s. What is the height of ball B when it encounters ball A.<\/span><\/p>\n

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

In solving the problem of vertical motion<\/a>, the vector quantity which direction upward is given a positive sign, the vector<\/a> quantity that direction downward is given a negative sign.<\/span><\/span><\/p>\n

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

Initial speed (vo<\/sub>) of ball A = 10 m\/s<\/span><\/p>\n

Time interval (t) of ball A = x<\/span><\/p>\n

Initial speed (vo<\/sub>) of ball B = 25 m\/s<\/span><\/p>\n

Time interval (t) of ball B = x – 1<\/span><\/p>\n

Acceleration due to gravity <\/a>(g) = -10 m\/s2 <\/sup>(given minus sign because the direction of gravity<\/a> is downward)<\/span><\/p>\n

Wanted :<\/u> The height of ball B when it encounters ball A (h)<\/span><\/p>\n

hA<\/sub> = hB<\/sub><\/span><\/p>\n

vo<\/sub> t + \u00bd g t2 <\/sup>= vo<\/sub> t + \u00bd g t2<\/sup><\/span><\/p>\n

10x + \u00bd (-10) x2 <\/sup>= 25 (x-1) + \u00bd (-10) (x-1)2<\/sup><\/span><\/p>\n

10x – 5x2 <\/sup>= 25 (x-1) – 5 (x-1)2<\/sup><\/span><\/p>\n

10x – 5x2 <\/sup>= 25x \u2013 25 – 5 (x2<\/sup>-2x+1)<\/span><\/p>\n

10x – 5x2 <\/sup>= 25x \u2013 25 \u2013 5x2 <\/sup>+ 10x \u2013 5<\/span><\/p>\n

10x – 5x<\/b>2<\/b><\/sup> – 25x + 25 + 5x<\/b>2<\/b><\/sup> – 10x + 5 = 0<\/span><\/p>\n

– 5x2<\/sup> + 5x2 <\/sup>+ 10x \u2013 25x \u2013 10x + 25 + 5 = 0<\/span><\/p>\n

10x \u2013 25x \u2013 10x + 25 + 5 = 0<\/span><\/p>\n

\u2013 25x + 25 + 5 = 0<\/span><\/p>\n

\u2013 25x + 30 = 0<\/span><\/p>\n

\u2013 25x = – 30<\/span><\/p>\n

x = -30\/-25<\/span><\/p>\n

x = 1.2 seconds<\/span><\/p>\n

Time interval ball A in air before it encounters ball B = 1.2 seconds<\/span><\/p>\n

Time interval ball B in air before it encounters ball A = 1.2 seconds \u2013 1 seconds = 0.2 seconds.<\/span><\/p>\n

The height of ball A when it encounters ball B :<\/span><\/p>\n

h = vo<\/sub> t + \u00bd g t2 <\/sup>= (10)(1.2) + 1\/2 (-10)(1.2)2 <\/sup>= 12 \u2013 5(1.44) = 12 \u2013 7.2 = 4.8 meter<\/b>s<\/b><\/span><\/p>\n

The height of ball B when it encounters ball A :<\/span><\/p>\n

h = vo<\/sub> t + \u00bd g t2 <\/sup>= (25)(0.2) + 1\/2 (-10)(0.2)2 <\/sup>= 5 \u2013 5(0.04) = 5 \u2013 0.2 = 4.8 meter<\/b>s<\/b><\/span><\/p>\n

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1. Question:<\/strong> What is meant by vertical motion?<\/span><\/p>\n

Answer:<\/strong> Vertical motion refers to the movement of an object upward or downward, typically under the influence of gravitational force.<\/span><\/p>\n

2. Question:<\/strong> How is acceleration due to gravity (g) significant in vertical motion?<\/span><\/p>\n

Answer:<\/strong> All objects near Earth’s surface experience a constant acceleration, \ufffd<\/span>g<\/span><\/span><\/span><\/span><\/span>, which is approximately 9.81 m\/s\u00b2 downward.<\/span><\/p>\n

3. Question:<\/strong> Can an object have an initial velocity in vertical motion?<\/span><\/p>\n

Answer:<\/strong> Yes, objects can have an initial upward or downward velocity when their vertical motion starts.<\/span><\/p>\n

4. Question:<\/strong> What happens to the velocity of a freely falling object?<\/span><\/p>\n

Answer:<\/strong> The velocity of a freely falling object increases by approximately 9.81 m\/s every second due to Earth’s gravity.<\/span><\/p>\n

5. Question:<\/strong> How is the time of ascent related to the time of descent for a vertically thrown object?<\/span><\/p>\n

Answer:<\/strong> For an object thrown upward and then allowed to fall back, the time of ascent equals the time of descent.<\/span><\/p>\n

6. Question:<\/strong> What is the velocity of an object at its maximum height?<\/span><\/p>\n

Answer:<\/strong> At maximum height, an object’s vertical velocity becomes zero before it starts descending.<\/span><\/p>\n

8. Question:<\/strong> How does air resistance affect vertical motion?<\/span><\/p>\n

Answer:<\/strong> Air resistance opposes motion, reducing acceleration and terminal velocity for falling objects.<\/span><\/p>\n

9. Question:<\/strong> What is terminal velocity?<\/span><\/p>\n

Answer:<\/strong> Terminal velocity is the constant maximum velocity reached by a falling object when air resistance equals the force of gravity.<\/span><\/p>\n

10. Question:<\/strong> Can an object have negative acceleration during upward motion?<\/span><\/p>\n

Answer:<\/strong> Yes, when an object moves upward against gravity, it has a negative acceleration equal to -g.<\/span><\/p>\n

12. Question:<\/strong> Why is the acceleration negative for objects thrown upward?<\/span><\/p>\n

Answer:<\/strong> Because acceleration due to gravity acts downward, it’s considered negative for objects moving in the opposite direction.<\/span><\/p>\n

14. Question:<\/strong> What is free fall?<\/span><\/p>\n

Answer:<\/strong> Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.<\/span><\/p>\n

15. Question:<\/strong> How does the motion of an object differ when thrown downward versus when dropped?<\/span><\/p>\n

Answer:<\/strong> Both experience acceleration due to gravity. However, an object thrown downward has an additional initial velocity, making it reach the ground faster than one simply dropped.<\/span><\/p>\n

16. Question:<\/strong> What factors affect an object’s terminal velocity?<\/span><\/p>\n

Answer:<\/strong> Factors include object’s mass, shape, surface area, and the medium’s density and viscosity it’s falling through.<\/span><\/p>\n

17. Question:<\/strong> Does an object in vertical motion possess kinetic and potential energy?<\/span><\/p>\n

Answer:<\/strong> Yes, an object’s kinetic energy increases as it falls, while its potential energy decreases, and vice-versa during ascent.<\/span><\/p>\n

18. Question:<\/strong> Why does an object’s velocity change during vertical motion?<\/span><\/p>\n

Answer:<\/strong> The gravitational force causes a constant acceleration, changing the object’s velocity until it reaches terminal velocity or changes direction.<\/span><\/p>\n

19. Question:<\/strong> Can vertical motion be described as uniformly accelerated motion?<\/span><\/p>\n

Answer:<\/strong> Yes, in the absence of air resistance, vertical motion under gravity is uniformly accelerated with an acceleration of g<\/span><\/span><\/span><\/span><\/span>.<\/span><\/p>\n

20. Question:<\/strong> How is the conservation of energy principle applied to vertical motion?<\/span><\/p>\n

Answer:<\/strong> The sum of kinetic and potential energy remains constant during vertical motion, assuming no energy loss to air resistance.<\/span><\/p>\n

Understanding vertical motion is essential in classical mechanics and has practical applications ranging from sports science to engineering and safety regulations.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

Vertical motion \u2013 problems and solutions 1. Ball A threw vertically upward with the speed of 10 m\/s. 1 second later, from the same position, Ball B is thrown vertically upward at the same path, with the speed of 25 m\/s. What is the height of ball B when it encounters ball A. Solution : … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","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":"Vertical motion \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-2419","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\/2419","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=2419"}],"version-history":[{"count":2,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2419\/revisions"}],"predecessor-version":[{"id":8570,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2419\/revisions\/8570"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=2419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=2419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=2419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}