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