A Projectile Is Launched from the Surface of a Planet $\left[\frac{4 G M R}{3 R}\right]^{1 / 2}$

question 39

Multiple Choice

A projectile is launched from the surface of a planet (mass = M, radius = R) . What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

• A) \(\left[\frac{4 G M R}{3 R}\right]^{1 / 2}\)
• B) \(\left[\frac{8 G M R}{5 R}\right]^{1 / 2}\)
• C) \(\left[\frac{3 G M R}{2 R}\right]^{1 / 2}\)
• D) \(\left[\frac{5 G M R}{3 R}\right]^{1 / 2}\)
• E) \(\left[\frac{G M}{3 R}\right]^{1 / 2}\)

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Definitions:

Emotional Connection

A bond formed through feelings of affection, empathy, or shared experiences, leading to a deeper understanding and relationship between people.

Fearful Attachment

Attachment style with high anxiety and high avoidance.

High Anxiety

A state characterized by excessive and persistent worry and fear about everyday situations, often to an intensity that disrupts daily functioning.

High Avoidance

Involves a tendency to steer clear of stressful or threatening situations as a way to manage anxiety and fear.