Answer :

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 = vcosβ


y component of velocity = vsinβ


x component of acceleration = gsinα


y component of acceleration = gcosα


t is the time of flight


Lets first find part b.



(b) Displacement in y direction is 0.


By 2nd kinematic equation in y-direction,





(a) By 2nd kinematic equation in x-direction,



Substituting the value of t in the above equation.





(c) In order to find the value of for which range is maximum,


We need to maximize


Now,







For to be maximum, , should be maximum and the maximum value of sin(θ) is 1.


Therefore,





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