Escape velocity given at an angle

Question

We know that the escape velocity of Earth is about 11.2Km/s but what if we give that same velocity to an object at any angle let's just take 30° will it still escape from Earth's gravitational field or not

Answer 1

Escape velocity is not dependent on direction. It was initially calculated using conservation of energy (setting kinetic energy equal to potential energy).

Since energy is a scalar quantity, the angle $\theta$ that an object is launched at will not change the escape velocity.

So $v_{escape} = 11.2 $ km/s