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Projectile Slant Range

A projectile is any object thrown into space (empty or not) by the exertion of a force. The projectile slant range describes the final distance of that projectile under the influence of gravity along a nonhorizontal surface.

The slant range equals the product of the cosine squared of the release angle relative to the horizontal, the initial speed squared, the difference between the tangent of the release angle relative to the horizontal and the tangent of the slope angle, the square root of one plus the tangent squared of the slope angle, and twice the reciprocal of the acceleration due to gravity.

Formula

QuantityVariable[Subscript["R", "s"], "Length"] == Cos[QuantityVariable["α", "Angle"]]^2*Quantity[2, "StandardAccelerationOfGravity"^(-1)]*QuantityVariable["v", "Speed"]^2*(Tan[QuantityVariable["α", "Angle"]] - Tan[QuantityVariable["θ", "Angle"]])*Sqrt[1 + Tan[QuantityVariable["θ", "Angle"]]^2]

symbol description physical quantity
Rs slant range "Length"
α release angle relative to the horizontal "Angle"
v initial speed "Speed"
θ slope angle "Angle"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Projectile Slant Range"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Projectile Slant Range"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Projectile Slant Range"], {QuantityVariable[ \!\(\*SubscriptBox[\("R"\), \("s"\)]\),"Length"] -> Quantity[6.04`, "Meters"], QuantityVariable["\[Theta]","Angle"] -> Quantity[20, "AngularDegrees"]}]
Out[3]=

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