Hello!
A rocket with a mass of 10,000 kilograms is propelled upward with 8,000,000 joules of kinetic energy. The velocity of the rocket is meters/second.
Data:
KE (Kinetic Energy) = 8000000 Joules
m (mass) = 10000 Kg
v (speed) = ? (m/s)
Formula:
[tex]v=\sqrt{\dfrac{2KE}{m}}[/tex]
Solving:
[tex]v=\sqrt{\dfrac{2KE}{m}}[/tex]
[tex]v=\sqrt{\dfrac{2*8000000}{10000}}[/tex]
[tex]v = \sqrt{ \dfrac{1600\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0}{1\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0}}[/tex]
[tex]v = \sqrt{1600}[/tex]
[tex]\boxed{\boxed{v = 40\:m/s}}\Longleftarrow(velocity\:of\:the\:rocket)\:\:\:\:\:\:\bf\green{\checkmark}[/tex]
*** Another way to do:
Formula:
[tex]K_{E} = \dfrac{1}{2}*m*v^2[/tex]
Solving:
[tex]K_{E} = \dfrac{1}{2}*m*v^2[/tex]
[tex]8000000 = \dfrac{1}{2}*10000*v^2[/tex]
[tex]8000000*2 = 1*10000*v^2[/tex]
[tex]16000000 = 10000\:v^2[/tex]
[tex]10000\:v^2 = 16000000[/tex]
[tex]v^2 = \dfrac{1600\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0}{1\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0\diagup\!\!\!\!0}[/tex]
[tex]v^2 = 1600[/tex]
[tex]v = \sqrt{1600}[/tex]
[tex]\boxed{\boxed{v = 40\:m/s}}\Longleftarrow(velocity\:of\:the\:rocket)\:\:\:\:\:\:\bf\green{\checkmark}[/tex]
Answer:
The velocity of the rocket is 40 meters/second
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