Question

For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60$^{\circ}$ with the vertical, then escape velocity will be

• A. 11 km/s
• B. $11 \sqrt 3 \,km /s$
• C. $ \frac{11}{\sqrt 3 }\, km /s$
• D. 33 km/s

Answer 1

The Correct Option is A

The concept of escape velocity refers to the minimum speed an object must have to break free from the gravitational field of a celestial body without further propulsion. For Earth, this velocity is approximately calculated as follows:

Escape velocity v_e = \sqrt{\frac{2GM}{R}},

where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth. For Earth, this evaluates to approximately 11 \, \text{km/s}.

Importantly, escape velocity is independent of the direction or angle of launch. It is solely dependent on the mass and radius of the celestial body.

In the given question, a satellite is launched at an angle of 60° with the vertical. Even though the angle changes, the escape velocity remains constant due to its independence from the launch direction. Thus, launch angles do not affect the magnitude of the escape velocity.

Therefore, regardless of whether the satellite is launched vertically, at 60°, or any other angle, the required speed for escape remains unchanged, which is:

11 km/s

The correct option is 11 km/s.