[tex]a) E_c=\frac{1}{4}E_p\\ E_{p_o}=0\\E_{c_o}+ E_{p_o}=E_c+E_p<=>\frac{mv_o^2}{2}+0= \frac{1}{4}E_p+E_p<=>\frac{mv_o^2}{2}=\frac{5}{4}mgh|:\frac{m}{2}=>v_o^2=\frac{5}{2}gh=>h=\frac{2v_o^2}{5g}=\frac{2*60^2}{5*10}= 144 m\\ h=144 m[/tex]
[tex]b)h_{max}=\frac{v_o^2}{2g}=\frac{60^2}{2g}=\frac{3600}{20} =180 m\\h'=\frac{h_{max}}{5}=\frac{180}{5}=36 m\\ h'=36 m\\v'^2=v_o^2-2gh'=60^2-2*10*36=3600-720=2880=>v'=\sqrt{2880}=53,66 m/s\\v'=53,66 m/s[/tex]
[tex]c)v=0\\v=v_o-gt'<=>0=60-10t'=>t'=6 s\\t\in [6,7]s\\t_1=6s=>d_1=v_ot_1-\frac{gt_1^2}{2}=60*6-\frac{10*6^2}{2}=360-180=180 m\\t_2=7 s=>t_2=6s+1s=>d_2=d_1+d'\\v_0'=0\\d'=v_o't'+\frac{gt'^2}{2}=0+5*1^2=5 m\\ d_2=d_1+d'=180+5=185 m\\d=d_2-d_1=185-180=5 m\\d=5 m[/tex]
