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garik1379 [7]
3 years ago
8

A projectile is launched from the surface of a planet (mass = 15 x 1024 kg, radius = R = 9.6 x 106 m). What minimum launch speed

is required if the projectile is to rise to a height of 6R above the surface of the planet? Disregard any dissipative effects of the atmosphere. Put your answer in km/s. ​
Physics
2 answers:
Serjik [45]3 years ago
6 0

Answer:

The minimum launch speed is 13366.40 m/s.

Explanation:

Given that,

Mass of planet M=15\times10^{24}\ kg

Radius R= 9.6\times10^{6}\ m

Height = 6R

We need to calculate the speed

Using relation between gravitational force and total energy

-\dfrac{GMm}{6R+R}=\dfrac{1}{2}mv^2-\dfrac{GMm}{R}

\dfrac{}{}mv^2=\dfrac{GMm}{7R}-\dfrac{GMm}{R}

\dfrac{1}{2}mv^2=\dfrac{6GMm}{7R}

v^2=\dfrac{2\times6GM}{7R}

Put the value into the formula

v=\sqrt{\dfrac{2\times6\times6.67\times10^{-11}\times15\times10^{24}}{7\times9.6\times10^{6}}}

v=13366.40\ m/s

Hence, The minimum launch speed is 13366.40 m/s.

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5 0

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buena suerte y tuve que traducir esto
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