A Rocket Is Launched Vertically Upward with a Speed $v _ { 0 }$

Multiple Choice

A rocket is launched vertically upward with a speed $v _ { 0 }$ . Take the upward direction as positive and let the mass be m. Assume that the only force acting on the rocket is gravity, which is inversely proportional to the square of the distance from the center of the earth. Let $y ( t )$ be the distance from the center of the earth at time, $t$ . the correct differential equation for the position of the rocket is

A) $m \frac { d y } { d t } = v _ { 0 } - k / y ^ { 2 }$
B) $m \frac { d ^ { 2 } y } { d t ^ { 2 } } = - k / y ^ { 2 }$
C) $\frac { d y } { d t } = v _ { 0 } - k / y ^ { 2 }$
D) $\frac { d ^ { 2 } y } { d t ^ { 2 } } = - k / y ^ { 2 }$
E) none of the above