more questions on simple harmonic motion

Could someone check these for me? i was told to put g = 9.8 m/s for all calculus questions, and I think it's a bit ridiculous.

**1. A long jumper running at 8 m/s jumps into the air, rising to a height of 0.7 metres. What is the length of the jump. **

maximum height

$\displaystyle 0.7 = \frac{V^2sin^2\alpha }{2g} $

$\displaystyle 0.7 = \frac{8^2sin^2\alpha }{2\cdot 9.8}$

$\displaystyle 13.72 = 64sin^2\alpha$

$\displaystyle sin\alpha = 0.463006479$

$\displaystyle \alpha = 27^{\circ}{35}' $

Range

$\displaystyle \frac{V^2sin2\alpha }{9.8}$

$\displaystyle =\frac{ 64sin55^{\circ}{10}' }{9.8}$

$\displaystyle = 5.36 m$

**This is wrong. the answer says 5.29 m. **

**2. The velocity of a point moving along the x axis is given by **

$\displaystyle V^2 = 10 + 8x - 2x^2$

**Show that it is simple harmonic.**

$\displaystyle \ddot{x} = \frac{d}{dx}(\frac{1}{2}v^2)$

$\displaystyle = \frac{d}{dx}(\frac{1}{2}10 + 8x - 2x^2)$

$\displaystyle = \frac{d}{dx}5+4x - x^2$

$\displaystyle = 4 - 2x$

However this is not the form $\displaystyle -n^2x $

so how would I do this?

Thanks!!! (Rofl) You guys are really helpful!