PSAT Math Multiple-Choice Question 194: Answer and Explanation

Question: 194

A projectile is any moving object that is thrown near the Earth's surface. The path of the projectile is called the trajectory and can be modeled by a quadratic equation, assuming the only force acting on the motion is gravity (no friction). If a projectile is launched from a platform 8 feet above the ground with an initial velocity of 64 feet per second, then its trajectory can be modeled by the equation h = - 16 t² + 64 t + 8, where h represents the height of the projectile t seconds after it was launched. Based on this model, what is the maximum height in feet that the projectile will reach?

• A. 72
• B. 80
• C. 92
• D. 108

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Passport to Advanced Math/Quadratics

Getting to the Answer: The quadratic equation is given in standard form, so use the method of completing the square to rewrite the equation in vertex form. Then, read the value of k to find the maximum height of the projectile:

The vertex is (2, 72), so the maximum height is 72 feet, (A).