Two billiard balls are rolling on a flat table. One has velocity components and other has velocity components If both the balls start moving from the same point, then what is the angle between their paths? - Wired Faculty

Question

Wired Faculty App

Two billiard balls are rolling on a flat table. One has velocity components $straight v subscript straight x 1 end subscript equals 1 straight m divided by straight s semicolon space straight v subscript straight y 1 end subscript space equals space square root of 3 space straight m divided by straight s$ and other has velocity components $straight v subscript straight x 2 end subscript equals 2 space straight m divided by straight s semicolon space space space straight v subscript straight y subscript 2 end subscript space equals space 2 space straight m divided by straight s.$ If both the balls start moving from the same point, then what is the angle between their paths?

Solution

Let $straight theta subscript 1$ and $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ be the angles that the two balls make with X-axis.
Given, the velocity components of first ball are,
$space straight v subscript straight x 1 end subscript space equals space 1 space straight m divided by straight s$
$straight v subscript straight y 1 end subscript space equals space square root of 3 space space straight m divided by straight s$
Therefore, angle is given by,
$tanθ subscript 1 space equals space straight v subscript straight y 1 end subscript over straight v subscript straight x 1 end subscript equals fraction numerator square root of 3 over denominator 1 end fraction equals square root of 3$
$rightwards double arrow$ $straight theta subscript 1 space equals space 60 degree$
The velocity components of second ball are,
$straight v subscript straight x 2 end subscript space equals space 2 space straight m divided by straight s$ ,
$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
∴ angle is given by,
$tanθ subscript 2 equals straight v subscript straight y 2 end subscript over straight v subscript straight x 2 end subscript equals 2 over 2 equals 1$
$straight theta subscript 2 space equals space 45 degree$
The angle between the paths of two ball is equal to the angle between their velocity vectors.
∴ The angle between the paths of two balls is,
$straight theta subscript 1 minus straight theta subscript 2 equals 60 degree minus 45 degree space equals space 15 degree.$

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction