Range and Time of Flight on Inclined Plane Assignment Help

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Range and Time of Flight on Inclined Plane:

If from a point on the plane which is inclined at the angle b to horizon, a particle is projected having velocity u, at an angle a with horizontal, in a plane passing through the normal to inclined plane and the of greatest slope, then

1584_Range and Time of Flight on Inclined Plane.png

Note:  

  • The Range, time of flight and the maximum range down the plane can be obtained by putting -b for b.
  • For the given range and given velocity there are 2 different directions of projection which are inclined equally to the direction of projection for the maximum range.

Example:  If the maximum range of particle is R, show that greatest height which can be attained is 1/4R. A body can throw the ball 60 meters. How long is ball in the air, and what height does it attain.

Solution:        Let the particle be projected with the velocity v at the angle a  with horizontal.

                        Horizontal range = 1796_Range and Time of Flight on Inclined Plane1.png

                        Greatest height = 2330_Range and Time of Flight on Inclined Plane2.png

                        The range is maximum where sin2a = 1 => a = 45°

                       779_Range and Time of Flight on Inclined Plane3.png

                     Now R = 60 metres  Þ h = 15 metres

                      Now  time  t of  flight  = 739_Range and Time of Flight on Inclined Plane4.png

                     924_Range and Time of Flight on Inclined Plane5.png  =>        t = 3.5 sec aprox. 

 

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