3.89: a) The trajectory of the projectile is given by Eq. (3.27), with φ, θ + = α0 and the equation describing the incline is . tan θ x y = Setting these equal and factoring out the 0= x root (where the projectile is on the incline) gives a value for ;0 x the range measured along the incline is . cos ) ( cos ] tan ) [tan( 2 cos / 2 20 + θ-+ = θ φ θ φ θ g v θ x b) Of the many ways to approach this problem, a convenient way is to use the same sort of "trick", involving double angles, as was used to derive the expression for the range along a horizontal incline. Specifically, write the above in terms of φ, θ + = α as . ] sin cos cos cos [sin cos 2 2 2 20 θ α- = g v
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Cos, Trajectory of a projectile, Range of a projectile, Sin Cos, cos cos