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Physics LibreTexts

12.9: Summary

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This following table summarizes the formulæ for a projectile initially at the origin, fired with initial velocity v0 at an angle θ from the horizontal.

Table 9-1. Summary of formulæ for projectile motion.

Quantity Formula
x(t) x=(v0cosθ)t
y(t) y=12gt2+(v0sinθ)t
y(x) y(x)=(g2v20cos2θ)x2+(tanθ)x
Time in flight tf=2gv0sinθ
Range at angle θ R=v20gsin2θ
Max. range (at θ=45) Rmax=v20g
Angle needed to hit target at range R for fixed v0 θ=12sin1(gRv20)
Speed needed to hit target at range R for fixed θ v0=gRsin2θ
Max. altitude h=v20sin2θ2g
Speed needed to hit target at (xt,yt) for fixed θ (xt,yt) for fixed θ & v0=gxt2(tanθytxt)cos2θ
Angle needed to hit target at (xt,yt) for fixed v0 xtsin2θ2ytcos2θ=gx2tv20

Note that this last expression must be solved iteratively for θ.


12.9: Summary is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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