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 2^{nd} kinematic equation in y-direction,

(a) By 2^{nd} 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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