The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is

Escape velocity is defined as the minimum speed for an object to break away from the gravitational pull of a celestial body, say Earth. For Earth, this escape velocity is around 11.2 km/s. If a body is projected vertically upwards, reaching this speed enables it to overcome gravitational attraction without needing any further propulsion.

In the case of launching at an angle, the scenario is different. If the projection is made at an angle of 45 degrees with respect to the vertical, then the launch velocity would need to be adjusted so that the vertical component was equal to the escape velocity at the given point. With the Earth’s gravity present, this would ensure indefinite ascent of the body projected. For an angle of 45 degrees, a relation between the total velocity at launch and the escape velocity is critical.

More precisely, the launching speed required now becomes 11.2√2 km/s when launched at this angle of projection. The adjustment in this case will take into account both the need to maintain enough momentum upwards and the angle of projection. By attaining this higher speed, it ensures that the vertical component of the velocity is high enough to escape Earth’s gravitational pull. This shows how the launching angles impact significantly on the dynamics involved in achieving escape velocity.