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In long jumping, does it matter how high you jump? What factors determine the span of the jump?

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If an athlete takes jump with velocity u and at an angle θ with horizontal, then

\(H = \frac{u^2sin^2\theta}{2g}\)

and \(R=\frac{u^2\,sin\,2\theta}{g}\)

∴ \(\frac{R}{H}=\frac{u^2\,sin\,2\theta}{g}\times\frac{2g}{u^2sin^2\theta}\)

 = \(\frac{2\,sin\,2\theta}{sin^2\,\theta}=\frac{2\times2\,sin\,\theta\,cos\,\theta}{sin^2\,\theta}\)

 = 4 cot θ

or R = 4H cot θ

Thus, the span of the jump depends on the height of the jump and the angle at which the athlete jumps.

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