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    Mathematical Modelling - Projectile Motion

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    A projectile is fired with initial velocity v (LT^-1) at an angle θ (M^0L^0T^0) with the horizon. You may expect that the gravity acceleration g (LT^-2) affects R (L) .

    a) Use dimensional analysis to understand the dependence of R on v, g, and θ .

    b) Describe approximately the influence of θ on R .

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    Solution Preview

    Let, (i) R α va
    (ii) R α gb
    (iii) R α θ^c
    Combining all these factors, we get R = k vagbθc (1)
    where k is a dimensionless constant ...

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