Question

You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem:mearth = 5.9742 x 1024 kgrearth = 6.3781 x 106 mmmoon = 7.36 x 1022 kgrmoon = 1.7374 x 106 mdearth to moon = 3.844 x 108 m (center to center)G = 6.67428 x 10-11 N-m2/kg2On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?

Answer 1

Answer:

The answer is 5102,91 m.

Explanation:

To find escape velocity:

$\frac{1}{2} mV^{2} =G\frac{Mm}{r^{2} }$. Therefore:

$V=\sqrt{\frac{2GM}{r} }$

Using the necessary informations:

$5534=\sqrt{\frac{2(6,67428.10^{-11)(5,9742.10^{24}) } }{r}}$

as we solve the equation we find $r=5102,91m$