For a satellite escape velocity is 11 km / s. If the satellite is launched at an angle of 60^∘

step 1 So the question is for a satellite escape velocity is 11 km per second. If satellites launch at

For a satellite escape velocity is 11 km / s. If the...

For a satellite escape velocity is $11 \mathrm{~km} / \mathrm{s}$. If the satellite is launched at an angle of $60^{\circ}$ with the vertical, then escape velocity will be (a) $11 \mathrm{~km} / \mathrm{s}$ (b) $11 \sqrt{3} \mathrm{~km} / \mathrm{s}$ (c) $\frac{11}{\sqrt{3}} \mathrm{~km} / \mathrm{s}$ (d) $33 \mathrm{~km} / \mathrm{s}$

For a satellite escape velocity is $11 \mathrm{~km} / \mathrm{s}$. If the satellite is launched at an angle of $60^{\circ}$ with the vertical, then escape velocity will be
(a) $11 \mathrm{~km} / \mathrm{s}$
(b) $11 \sqrt{3} \mathrm{~km} / \mathrm{s}$
(c) $\frac{11}{\sqrt{3}} \mathrm{~km} / \mathrm{s}$
(d) $33 \mathrm{~km} / \mathrm{s}$

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Key Concepts

Escape Velocity

Escape velocity is the minimum speed required for an object to escape from the gravitational influence of a celestial body without any further propulsion. It is determined by equating the object's kinetic energy to its gravitational potential energy, making it independent of the object’s mass.

Vector Decomposition

Vector decomposition involves breaking down a velocity vector into its components along specific directions, typically horizontal and vertical. When a satellite is launched at an angle, its velocity can be resolved into vertical and horizontal components using trigonometric functions, which is essential for understanding how much of the speed directly counteracts gravity.

Effective Velocity Component in Relation to Launch Angle

When an object is launched at an angle with respect to the vertical, only the vertical component of the velocity contributes directly to overcoming gravitational pull. This means that if the launch is not vertical, the initial speed must be higher to ensure that the vertical component meets or exceeds the escape velocity required to overcome gravity.

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