# Determine the mass of a spacecraft orbiting at a speed of 7.8 km / s if its kinetic speed is 2 * 10 ^ 11 J.

Given:
v = 7.8 km / s is the speed of the orbiting spacecraft;
E = 2 * 1011 Joules – the kinetic energy of the spacecraft.
It is required to determine m (kilogram) – the mass of the spacecraft.
Let’s convert the units of measurement of speed from km / s to meters per second:
v = 7.8 km / s = 7.8 * 1000 = 7800 m / s.
Then, to determine the mass, you must use the following formula:
E = m * v^2 / 2, from here we find that:
m = 2 * E / v^2 = 2 * 2 * 10^11 / (7800) ^2 = 4 * 10^11 / (6084 * 10^4) = 0.00066 * 10^7 = 6600 kilograms.
Answer: the mass of the spacecraft is 6600 kilograms.

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