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Sagot :
Givens.
• The mass of the ballon is 2.30 kg.
,• The height is 35.65 m.
First, find the final velocity when the balloon is at the bottom. Use a formula that relates height, initial speed, final speed, and gravity.
[tex]v^2_f=v^2_0+2gh[/tex]Where
• v_0 = 0 because the balloon starts from rest.
,• Gravity is g = 9.8 m/s^2.
,• h = 35.65 m.
Use all these magnitudes to find the final velocity v_f
[tex]\begin{gathered} v^2_f=0^2+2(9.8\cdot\frac{m}{s^2})(35.65m) \\ v^2_f=698.74m^2 \\ v_f=\sqrt[]{698.74m^2} \\ v_f\approx26.4(\frac{m}{s}) \end{gathered}[/tex]Once we have the velocity at the bottom, find the kinetic energy using its formula.
[tex]K=\frac{1}{2}mv^2[/tex]Where m = 2.30 kg, and v = 26.4m.s.
[tex]\begin{gathered} K=\frac{1}{2}\cdot(2.30\operatorname{kg})\cdot(26.4(\frac{m}{s}))^2 \\ K=1.15\cdot696.96J \\ K=801.5J \end{gathered}[/tex]Therefore, the kinetic energy at the bottom is 801.5 J.
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