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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The Answer of 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) $\left[\frac{G M}{3 R}\right]^{1 / 2}$

A Projectile Is Launched from the Surface of a Planet [4GMR3R]1/2\left[\frac{4 G M R}{3 R}\right]^{1 / 2}[3R4GMR​]1/2

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