A Rocket with Mass $m$ Is Launched Vertically Upward from the Surface of the Earth

Multiple Choice

A rocket with mass $m$ is launched vertically upward from the surface of the earth with a velocity $v _ { 0 }$ . Let $y ( t )$ be the distance of the rocket from the center of the earth at time $t$ . Assuming 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, the correct differential equation for the position of the rocket is

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