Em=13000 kJ = 13 000 000 J
m=2300 kg
v=270 km/h
h = ?
[tex]270 \ \frac{km}{h}=270*\frac{1000 \ [m]}{3600 \ [s]}=75 \ \frac{m}{s}[/tex]
[tex]E_m=E_p+E_k=mgh+\frac{mv^2}{2}\\ \\mgh=E_m-\frac{mv^2}{2}\\ \\h=\frac{E_m-\frac{mv^2}{2}}{mg}=\frac{13 \ 000 \ 000 \ [J]-\frac{2 \ 300 \ [kg]*(75 \ [\frac{m}{s}])^2}{2} }{2 \ 300 [kg]*10 \ [\frac{m}{s^2}]}=\frac{13 \ 000 \ 000-\frac{2 \ 300*5 \ 625}{2}}{23 \ 000}=\\ \\\approx283,97 \ m[/tex]
[tex]h=\frac{[J]-\frac{m^2}{s^2}}{[kg]*[\frac{m}{s^2}]}=\frac{[\frac{kg*m^2}{s^2}]-\frac{m^2}{s^2}}{\frac{kg*m}{s^2} } =\frac{[\frac{kg*m^2}{s^2}]}{\frac{kg*m}{s^2}}-\frac{\frac{m^2}{s^2}}{\frac{kg*m}{s^2}}=[m]-[m]=m[/tex]