PSAT Math Multiple-Choice Question 228: Answer and Explanation

Question: 228

Escape velocity is the speed that a traveling object needs to break free of a planet or moon's gravitational field without additional propulsion (for example, without using fuel). The formula used to calculate escape velocity is , where G represents the universal gravitational constant, m is the mass of the body from which the object is escaping, and r is the distance between the object and the body's center of gravity. Which equation represents the value of r in terms of v, G, and m ?

• A.
• B.
• C.
• D.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Passport to Advanced Math/Radicals

Getting to the Answer: Don't spend too much time reading the scientific explanation of the equation. Solve for r using inverse operations. First, square both sides of the equation to remove the radical. Then, multiply both sides by r to get the r out of the denominator. Finally, divide both sides by v²:

This matches (A).