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A particle is projected in air at an angle β to a surface which itself is inclined at an angle α to the horizontal. a) find an expression of range on the plane surface b) time of flight c) β at which range will be maximum
A particle is projected in air at an angle β to a surface which itself is inclined at an angle α to the horizontal. a) find an expression of range on the plane surface b) time of flight c) β at which range will be maximum
CBSE | Class 11 | Motion in a Plane | NCERT | Physics
A particle is projected in air at an angle β to a surface which itself is inclined at an angle α to the horizontal. a) find an expression of range on the plane surface b) time of flight c) β at which range will be maximum

Answer:

This problem has two solutions:
i)The point P where the particle impacts the plane is the parabola/straight line intersection. 
In other words, it’s not a straight line.
ii) It is possible to take the x- and y- directions perpendicular to the plane. 
So divide g (gravitational acceleration) into two halves. 
gx which is in-plane and gy which is perpendicular 
Now the challenge is two independent x and y motions with time as a shared parameter.
a) Time of flight, $T =$

2usin(α+β)gcosβ\frac{2 u \sin (\alpha+\beta)}{g \cos \beta}

b) Range down an inclined plane, $R =$

2u2sin(α+β)cosαgcos2β\frac{2 u^{2} \sin (\alpha+\beta) \cos \alpha}{g \cos ^{2} \beta}

c) Maximum grange down an inclined plane, Rmax =

u2g(1–sinβ)\frac{u^{2}}{g(1-\sin \beta)}
i

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