Ignore air friction for the following problem. If you throw a stone upwards with a speed greater than the escape speed, it will continue to move away from Earth forever and never return. The escape speed on Earth is 11.186 km/s. Now consider that you throw a stone directly in the direction of the Moon (it is ok to ignore the rotational motion of the Moon around the Earth). What is the minimum speed that you need to give the stone so that it makes it to the Moon?

It is recommended to carefully think about this problem and then use energy conservation to find a solution. Even for the minimum speed the stone will have a large velocity when it reaches the Moon. You can use the following data: mass of Earth is 5.972 10²⁴kg, mass of the Moon is 7.348 10²²kg, distance Earth-to-Moon is 384.4 10⁶m, radius of Earth is 6.371 10⁶m. The solution requires at least 4 correct digits.