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**1. The problem statement, all variables and given/known data**

A rock is thrown from a 1 meter height with a 35 degrees angle with horizontal. At x=64 m, its height is y=29 m. Find it's initial velocity.

**2. Relevant equations**

[tex]x=x_{{0}}+v_{{{\it x0}}}t+ 0.5\,a_{{x}}{t}^{2}[/tex]

[tex]y=y_{{0}}+v_{{{\it y0}}}t+ 0.5\,a_{{y}}{t}^{2}[/tex]

**3. The attempt at a solution**

Let F = initial velocity

then Vx0 = F cos 35

Vy0 = F sin 35

[tex]x=x_{{0}}+v_{{{\it x0}}}t+ 0.5\,a_{{x}}{t}^{2}[/tex]

[tex]64=F\cos \left( 35 \right) t[/tex]

[tex]t=64\,{\frac {1}{F\cos \left( 35 \right) }}[/tex]

[tex]y=y_{{0}}+v_{{{\it y0}}}t+ 0.5\,a_{{y}}{t}^{2}[/tex]

[tex]29=1+64\,\tan \left( 35 \right) - 10035.20000\,{\frac {1}{{F}^{2}

\left( \cos \left( 35 \right) \right) ^{2}}}[/tex]

solving for F gives 102 m/s

the answer in the book is 42 m/s

sorry i am new to latex