00:02Asalaamu alaykum dear viewers, dear viewers,
00:06जैसा के previous lecture में हमने types of vectors के बारे में study करी थी
00:11और आज हम resolution of vectors, means vector को जो तोड़ने का, means उनके components में तोड़ने का अमल है
00:22उसके बारे में हम आज study करेंगे
00:25So, resolution of vector क्या होता है?
00:30यह एक ऐसा process होता है, जिसमें किसी भी vector को उसके components में हम split करते हैं या break
00:39करते हैं
00:40Means, addition of vectors में हम क्या करते हैं?
00:43addition of vectors में हम components में से resultant obtain करते हैं
00:49लेकिन यहाँ पर हम क्या करते हैं?
00:52यहाँ पर resultant को हम उसके components में break करते हैं
00:56means resolution of vector is a reverse process of vector addition means vector addition
01:04ke reverse process ko bhi hem resolution of vector ke saktay so resolution of vector
01:11ko kaisa define kereenge the splitting of a single vector
01:32into its rectangular components such as horizontal
02:03component and vertical component is known as resolution
02:27of vector means resolution of vector aisa process hota is
02:33jis may hem a single vector ko uske rectangular components me break
02:39means split so us process ko hong kya kertai resolution of vectors ya is ko hong aise bhi define
02:47kar saktay and the reverse
02:57the reverse process of vector addition of vector addition is also known as resolution
03:24of a vector means vector addition ke reverse process ko bhi hem resolution of vector ke saktay
03:37ab ab kaisa am a single vector ko uske components me means rectangular components me break kareenge
03:54suppose this is x axis
03:56and this is y axis and this is y axis suppose vector v is lying along x axis suppose vector
04:10v is lying along x axis
04:14and this is the vector vector vector v is lying along x axis so we can break kareenge
04:24so we can break kareenge
04:26so we can break kareenge
04:44means x means x means x means velocity vector v vector means velocity vector . which is vx which is
04:53vx
04:53and y axis
04:54means y axis is kareenge
04:58means y axis is kareenge
04:59so we can break kareenge
05:12original component or vertical component
05:15in both components
05:16we call rectangular components
05:19these are known as
05:20rectangular components
05:21and the angle between
05:23the rectangular components is
05:2590 degrees
05:28rectangular components
05:30which angle is between
05:3290 degrees
05:35here we call
05:38theta
05:39so
05:41vector v
05:42we call it
05:43x and y components
05:44split
05:45break
05:47so this process
05:49we call it
05:50resolution of vector
05:52we call it
05:52for horizontal components
06:07horizontal component
06:09we call it
06:12we call it
06:13we call it
06:14we call it
06:16cos theta
06:17is equal to base upon hypotenuse
06:22cos theta is equal to base upon hypotenuse
06:25so here we call it
06:29this is base
06:30and this is perpendicular
06:32and this is hypotenuse
06:35this is hypotenuse
06:37this is hypotenuse
06:38this is base
06:39and this is perpendicular
06:41we call it
06:42so base
06:44so base
06:44here we call it
06:45vx
06:46so vx is base
06:48and hypotenuse is v
06:51so v
06:52we have to find the horizontal component
06:56so here we divide
06:58and if we divide
06:58then we call it
07:00cos theta
07:01multiply
07:02so it will be
07:04v cos
07:06theta
07:06is equal to
07:07vx
07:09or
07:09we call it
07:11vx is equal to
07:13v cos
07:14theta
07:17this is
07:18horizontal component
07:19now we call it
07:21vertical component
07:22means v y
07:23we call it
07:23for vertical component
07:34vertical component
07:35vertical component
07:35we call it
07:37we call it
07:38we call it
07:39we call it
07:39sin theta
07:40is
07:43sin theta
07:45is equal to
07:47perpendicular upon
07:49hypotenuse
07:50sin theta
07:51is equal to
07:52perpendicular upon
07:53hypotenuse
07:54is equal to
07:55here we call it
07:56perpendicular
07:57y component
07:58of velocity
07:59so v y
08:03divided by
08:06hypotenuse
08:07hypotenuse
08:07is v
08:08so here we call it
08:10we call it
08:11so we have to find
08:12y component
08:14of velocity
08:15so
08:16v
08:16v
08:17here we call it
08:18divide
08:18so
08:20v
08:21sin theta
08:23is equal to
08:25v y
08:26or
08:27we call it
08:30v y
08:32is equal to
08:33v
08:33v
08:34sin theta
08:36so
08:37this is
08:37the
08:38vertical component
08:39of
08:40v
08:41means of
08:42velocity
08:43here
08:44we
08:44don't
08:44here
08:44here
08:45we
08:45don't
08:45see
08:45here
08:46we
08:46don't
08:47here
08:47we
08:47see
08:48here
08:48see
09:02this is
09:03a horizontal
09:03component
09:04and
09:04this is
09:05a
09:05vertical
09:06of
09:06different
09:07angles
09:07x
09:09or y
09:09components
09:10value
09:10from
09:11some examples
09:15for example
09:16if
09:16angle is
09:180
09:19degrees
09:20and the value
09:21of v
09:22means the magnitude
09:23of v
09:24is
09:245
09:26meter
09:26per second
09:27this is
09:28example
09:29v
09:29value
09:305
09:31meter
09:31per second
09:310
09:32degree
09:33per
09:33horizontal
09:34component
09:36is
09:37v x
09:38is equal
09:39to
09:39v cos theta
09:41so
09:42v x
09:43will be equal
09:44to
09:44the value
09:45of v
09:46is
09:465
09:47multiplied
09:48with cos theta
09:49cos
09:50the value of
09:52theta is
09:530 degree
09:54as we know that
09:55the value of
09:58cos 0 degree
09:59is 1
10:01so
10:02v x
10:03will be equal
10:04to
10:055
10:06yahan par cos
10:070 degree ki jage par
10:09am 1
10:09lekhengi
10:105 into 1
10:11so v x
10:12will be equal to
10:135
10:14meter per second
10:16because
10:165 into 1
10:17it will be 5
10:18so
10:19horizontal component
10:200 degree
10:21angle
10:22angle
10:225 meter per second
10:25vertical component
10:26else
10:27vertical component
10:28v y
10:29is equal to
10:31v
10:32sin theta
10:36so
10:41v y
10:42will be equal to
10:55theta
10:56theta is 0
10:57so sin 0 degree
11:01so sin 0 degree
11:02so v y will be equal to
11:03is the value of sin 0 degree is 0
11:10sin 0 degree ka jage value hota hai go 0 hota hai
11:14so it will be 5 into 0 it will be 5 into 0 so y components will be obtained as
11:245 into 0 will be 0
11:26meter per second
11:29so
11:29so
11:30so
11:30so
11:31so
11:31so
11:31so
11:31so
11:35so
11:47so
11:48so
11:500 degree
11:500 degree
11:510 degree angle
11:520 degree angle per horizontal component maximum ho jage ga or vertical component is zero ho jage ga
11:59as a
11:59as a
12:00a
12:00a
12:00a
12:00a
12:00a
12:00a
12:00a
12:01a
12:01a
12:01a
12:03a
12:04a
12:05a
12:06a
12:07a
12:07a
12:08is equal to V cos theta. So, Vx will be equal to, the value of V is 5 multiplied with
12:18cos,
12:20the value of theta is 90. As we know that cos 90 degrees is equal to 0. Cos 90 degrees
12:29ka value hota hai wo konsa hota hai? 0 hota hai. So, horizontal component means Vx will
12:36be 5 multiplied with cos 90. The value of cos 90 is 0. So, into 0. So, 5 into 0
12:45will
12:45be 0 meter per second. Horizontal component 90 degrees per joh hume mila wo 0 mila. Acha
12:54ab Y components, Y component joh velastica hume konsa hume lega at 90 degrees. So, Vy
13:03is equal to V sin theta. Vy is equal to V sin theta, this is the y component. So, Vy
13:12is equal
13:13to, the value of V is 5. So, 5 multiplied with this sin, the value of theta is 90. So,
13:2490
13:24degrees is sin 90 degrees is equal to 1. Means the value of sin 90 degrees is 1. So, Y
13:37component
13:38will be obtained as 5 into sin 90 degrees ki jagay par hume 1 put karen gai. So, multiplied
13:44with 1. So, Y component will be obtained as 5 into 1, it will be 5 meter per second. So,
13:52this
13:52is the vertical component of velocity. Dekhi, jab angle 90 degrees ho, to horizontal components
14:01kya ho jayega 0. Horizontal component will be 0 and what will be the vertical component? Vertical
14:10component will be maximum. Means 90 degrees per jab angle 90 degrees ho, to horizontal component
14:210 ho jayega, or vertical component maximum ho jayega. Jab angle 0, to 0 angle per horizontal component
14:31maximum maximum ho jayega, or vertical component 0 ho jayega. Iskara matlab hai, kya ho jayega,
14:41or vertical component 0 ho jayega, or vertical component 0 ho jayega. Like in 90 degrees per
14:49horizontal or vertical component, if angle 0 ho jayega, or vertical component is maximum ho jayega.
15:06If angle is, means if theta is 45 degrees, and the value of V is 10 meter per second. Acha,
15:24so what will be horizontal and vertical component is horizontal component Vx is equal to V cos theta. So,
15:33Vx is equal to, the value of V is 10 multiplied with cos, the value of 45 means theta is
15:4245 degrees. So,
15:47Vx is the value of cos 45 degrees is 0.707. So, Vx will be obtained as 10 multiplied with
15:59the value of cos 45 degrees is 0.707. So, 0.707
16:06lichigium. So, when we will multiply 10 with this, we will get Vx is 7.07 meter per second.
16:19Yeh me horizontal component obtained huwa velocity ga. Now, vertical component. As vertical component Vy is equal to
16:29V sin theta. So, Vy will be equal to V sin theta. Horizontal component Vx is equal to V cos
16:34theta and vertical component Vy is equal to V sin theta. So, Vy will be equal to the value of
16:43V is 10, 10 meter per second multiplied with this sin theta.
16:50The value of theta. The value of theta is 45 degrees. 45 degrees. As the value of sin 45 degrees
17:00is 0.707. Sin 45 degrees ka be value 0.707a. So, vertical component will be obtained as 10 multiplied
17:14with the value of sin 45 degrees is 0.707a.
17:20So, 10 multiplied with 0.707. So, 10 multiplied with 0.707. Then, Vy will be obtained as 7.07
17:28meter per second.
17:33So, this is the horizontal component and this is vertical component. Seekhi. 45 degrees par jo horizontal component ka value
17:44hamei obtained huwa hai.
17:46Seem hi value hamei. Seem hii value hamei vertical component ka obtained huwa hai. Means,
17:51means, hamei kaih saakta hai hai ke 45 degrees angle par. Means, jab angle 45 degrees ho ho,
17:59toh, us par dono components equal ho jayenge. Means, dono components ke values kya ho jayenge? Same. Means, we can
18:07say that at 45 degrees,
18:09means, it 45 degrees, Vx will be equal to Vy. Means, jab angle ho 45 degrees,
18:23toh, horizontal components barabar ho jayega, equal ho jayega, kiske vertical component ke.
18:30So, dear students, that was about today's topic. Thank you. Allafez.
