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
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 =
Greatest height =
The range is maximum where sin2a = 1 => a = 45°
Now R = 60 metres Þ h = 15 metres
Now time t of flight =
=> t = 3.5 sec aprox.
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