Insertion Sort

incline) gives a value for x0 ; the range measured along the incline is ⎡ 2v 2 ⎤ ⎡ cos 2 (θ + φ) ⎤ x / cos θ = ⎢ 0 ⎥ [tan(θ + φ) − tan θ ] ⎢ ⎥ . ⎣ g ⎦ ⎣ cos θ ⎦ (b) Of the many ways to approach this problem, a convenient way is to use the same sort of substitution, involving double angles, as was used to derive the expression for the range along a horizontal incline. Specifically, write the above in terms of α = θ + φ, as 2 ⎡ 2v0 ⎤ 2 R=⎢ ⎥ [sin α cos α cosθ − cos α sin θ ] . 2 ⎣ g cos θ ⎦

incline) gives a value for x0 ; the range measured along the incline is ⎡ 2v 2 ⎤ ⎡ cos 2 (θ + φ) ⎤ x / cos θ = ⎢ 0 ⎥ [tan(θ + φ) − tan θ ] ⎢ ⎥ . ⎣ g ⎦ ⎣ cos θ ⎦ (b) Of the many ways to approach this problem, a convenient way is to use the same sort of substitution, involving double angles, as was used to derive the expression for the range along a horizontal incline. Specifically, write the above in terms of α = θ + φ, as ⎡ 2v02 ⎤ 2 R=⎢ ⎥ [sin α cos α cosθ − cos α sin θ ]…