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Projectile Motion on an Inclined Plane

Let a particle be projected up with a speed u from an inclined plane which makes an angle α with the horizontal velocity of projection and makes an angle θ with the inclined plane.
 
We have taken reference x-axis in the direction of plane (Fig. 11). Hence, the components of initial velocity parallel and perpendicular to the plane are equal to u cos θ and u sin θ, respectively, i.e., 30291.png and u = u sin θ.
 
30284.png
Fig. 11
 
The component of g along the plane is g sin α and perpendicular to the plane is g cos α as shown in Fig. 11, i.e., 30277.png and a = g cos α. Therefore, the particle decelerates at a rate of g sin α as it moves from O to P.

Time of flight

We know for oblique projectile motion, 30271.png
or we can say 30265.png 30258.png
 
∴ Time of flight on an inclined plane

Maximum height

We know for oblique projectile motion, 30252.png
or we can say 30246.png
 
∴ Maximum height on an inclined plane 30240.png

Horizontal range

30234.png
  • Maximum range occurs when 30228.png
  • The maximum range along the inclined plane when the projectile is thrown upward is given by
     
    30222.png
  • The maximum range along the inclined plane when the projectile is thrown downward is given by
     
    30216.png




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