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For an object of mass the energy required to escape the Earth's gravitational field is GMm / r, a function of the object's mass (where r is the radius of the Earth, G is the gravitational constant, and M is the mass of the Earth, M =5.9736Ã10 24 kg).or a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is 253.5 am/s (8 nanometers per year) faster than the escape velocity relative to the mutual center of mass.
Escape velocity depends on G not g, so increase or decrease in Earth's gravitational pull doesn't matter. Hence, a launch from Mt. Everest will need less that 11.2 km/s as its increasing the radius by roughly 8 km. Now given the huge mass of earth, the change is negligible. Notice that escape velocity increases at higher latitudes, hence, launch pads are kept as close to equator as possible.