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

question 36

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

---

Definitions:

Spot Trade

A transaction for the immediate purchase or sale of a financial instrument.

Official Exchange Rate

The official exchange rate is the rate at which a country's central bank will exchange its currency for foreign currency.

Agreement

An agreement is a mutual understanding or arrangement between two or more parties, often legally binding, about their rights and responsibilities regarding a particular deal or situation.

Dollar Strengthened

A condition where the U.S. dollar increases in value compared to other currencies in the global market.