problem03_90

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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3.90: As in the previous problem, the horizontal distance x in terms of the angles is . ) ( cos 1 2 ) tan( tan 2 2 0 φ θ φ θ θ + - + = v gx Denote the dimensionless quantity 2 0 2 / v gx by ; β in this case . 2486 . 0 ) m/s 0 . 32 ( 2 30.0 m)cos 0 . 60 )( m/s 80 . 9 ( 2 2 = ° = β The above relation can then be written, on multiplying both sides by the product , ) cos( cos φ θ θ + , ) cos( cos cos ) sin( ) cos( sin φ θ θ β θ φ θ φ θ θ + - + = + and so . ) cos( cos sin ) cos( cos ) sin( φ θ θ β θ φ θ θ φ θ + = + - + The term on the left is , φ θ φ θ sin ) ) sin(( = - + so the result of this combination is . cos ) cos( sin θ β φ θ φ = + Although this can be done numerically (by iteration, trial-and-error, or other methods), the expansion )) sin( ) (sin( cos sin
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• Dimensionless quantity, product cos cos

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