In long jumping, does it matter how high you jump? What factors determ

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

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

Answer»

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.