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    The ceiling of a long hall is 25m high. What is the maximum horizontal distance that a ball thrown with speed of 40 m/s can go without hitting the ceiling of the hall?
    Height of the ceiling = 25 m = MAximum height attained by the ball. 

    Velocity of the ball, u = 40 m/s

    Maximum height is given by, 

    i.e., 

    ∴        

               

    ∴ Maximum horizontal distance,

          
                                               
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    A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?
    Horizontal range is maximum if the angle of projection is 45°.

    Horizontal range in this case is given by,

                    

    So,      

    ∴           

    If the cricketer throws the ball vertically upward then it will attain the maximum height from the ground.

    ∴      , is the height of the ball from the ground. 
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    In a harbour, wind is blowing at the speed of 72 km/h and a flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
    Let east be taken along X-axis and north along Y-axis
    Let east be taken along X-axis and north along Y-axisVelocity of wind
    Velocity of wind is,
                    stack straight v subscript straight w with rightwards arrow on top space equals space 72 space km divided by hr space along space NE space direction
                          equals 72 space cos space 45 degree space straight i with hat on top space plus space 72 space sin space 45 degree space straight j with hat on top
                           equals 50.9 straight i with hat on top space plus space 50.9 straight j with hat on top
    Velocity of boat,  <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>
                                       equals 51 straight j with hat on top
    The flag flutters in the direction of relative velocity of wind relative to boat. The relative velocity of wind w.r.t. the boat is
    straight v with rightwards arrow on top subscript wb equals straight v with rightwards arrow on top subscript straight w minus straight v with rightwards arrow on top subscript straight b equals 50.9 straight i with hat on top minus 0.1 straight j with hat on top
    Since Y component of velocity is approximately zero, hence the flag will flutter almost due east.
                            
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    An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900
    km/h. Compare its centripetal acceleration with the acceleration due to gravity

    Radius of the loop, r = 1 km = 1000 m 

    Speed of the aircraft, v = 900 km/h = 900 × 5 / 18  =  250 m/s

    Centripetal acceleration, straight a subscript straight c space equals space straight v squared over straight r
    = fraction numerator left parenthesis 250 right parenthesis squared over denominator 1000 end fraction space equals space 62.5 space m divided by s squared

    Acceleration due to gravity, g = 9.8 m/s2

    Therefore, 

    ac / g = 62.5 / 9.8  =  6.38
    ac = 6.38 g, is the required centripetal acceleration. 
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    A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

    Let, u be the velocity of projection of the ball. The motion of the ball is along vertical direction. 

    The ball will cover maximmum horizontal distance when angle of projection with horizontal is 45o. 

     

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