The range R of a projectile propelled downward from the top of an inclined plane at an angle to the inclined plane is given by

Where is the initial velocity of the projectile, is the angle the plane makes with respect to the horizontal, and g is acceleration due to gravity.

(a) Show that for fixed v₀ and the maximum range down the incline is given by

(b) Determine the maximum range if the projectile has an initial velocity of 50 meters/second, the angle of the plane is ϕ = 35º, and g = 9.8 meter/second².

2v3 sin 0 cos(0 4) R(0) .2 COS g cos? o v g(1 sin ) R, 'max