Let’s consider the X-axis parallel to the inclined surface and Y-axis perpendicular to it. v be the speed of the projectile.
Range=R, x component of velocity = vsinθ
y component of velocity = vcosθ
x component of acceleration = gsinθ
y component of acceleration = gcosθ
There is no displacement in the y direction.
By 2nd kinematic equation in y-direction,
Now let’s calculate the distance along the plane the particle hit = R,
By 2nd kinematic equation in x-direction,
Substituting the value of t in the above equation.
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