Question

A body of mass 10 kg explodes into three masses in the ratio 2 : 3 : 5. Two light fragment fly off at right angle with velocity 12m/ s and 8m/s. Find the velocity of third fragment.

Solution

After explosion,
Let 2 kg mass after explosion fly off along X-axis and 3 kg mass fly off along Y-axis perpendicular to direction of motion of 2 kg mass.
Suppose the velocity of third fragment after explosion is $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
∴ Momentum of 2 kg mass is,
$stack straight P subscript 1 with rightwards arrow on top space equals space straight m subscript 1 stack straight v subscript 1 with rightwards arrow on top space equals space 2 cross times 12 straight i with hat on top space equals space 24 straight i with hat on top space space Ns$
Momentum of 3 kg mass is,
 $stack straight P subscript 2 with rightwards arrow on top space equals space straight m subscript 2 stack straight v subscript 2 with rightwards arrow on top space equals space 3 cross times 8 straight j with hat on top space equals space 24 space straight j with hat on top space space Ns$
Momentum of 5 kg mass is,
 $stack straight P subscript 3 with rightwards arrow on top space equals space straight m subscript 3 space stack straight v subscript 3 with rightwards arrow on top space equals space 3 cross times straight v with rightwards arrow on top space equals space 3 straight v with rightwards arrow on top space space Ns$
According to the law of conservation of linear momentum,
 $stack straight P subscript 1 with rightwards arrow on top plus stack straight P subscript 2 with rightwards arrow on top plus stack straight P subscript 3 with rightwards arrow on top space equals space 0$
$rightwards double arrow$ $24 straight i with hat on top space plus space 24 straight j with hat on top space plus space 5 straight v with rightwards arrow on top space equals space 0$
$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
∴ $space space space open vertical bar straight v with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 4.8 right parenthesis squared plus left parenthesis 4.8 right parenthesis squared end root$