In Scenario 1, a student standing on the ground throws a ball horizontally with an initial speed of v₀ = 8.0 m/s from a height of h = 2.0 m above the ground, as shown in Figure 1. The ball lands on the ground a horizontal distance d₁ from the point directly below where it was released. Air resistance is negligible.
Figure 1. Ball thrown horizontally
Figure 2. Cart and ball motion
A.
Indicate whether d₁ is greater than, less than, or equal to d₂ by writing one of the following in your answer booklet.
• d₁ > d₂
• d₁ < d₂
• d₁ = d₂
Justify your answer in terms of ALL components of the ball's motion as observed from the ground reference frame in each scenario (see Figure 1 and Figure 2). Use qualitative reasoning beyond referencing equations.
B.
Starting with kinematic principles, derive an expression for the horizontal distance d the ball travels before landing on the ground. Express your answer in terms of vₓ, h, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the general case where a ball is thrown horizontally with an initial horizontal velocity component vₓ from a height h above the ground.
C.
Indicate whether the expression for the distance d you derived in part B is or is not consistent with the claim made in part A. Briefly justify your answer by referencing your derivation in part B and the relationship between the horizontal velocity components in the two scenarios as observed from the ground reference frame.
What the Qualitative/Quantitative FRQ asks
The Qualitative/Quantitative Translation (QQT) question is FRQ 4 on the AP Physics 1 exam. You compare two situations and justify your answer in words, derive an expression, then check whether the expression supports your answer.
A comparison justified with physics reasoning, not just equations
3 pts
B
Part B: Derivation
An expression derived from a physics principle
3 pts
C
Part C: Consistency
Usually whether your expression supports your answer to part A
2 pts
How Qualitative/Quantitative FRQ practice works
Each question follows the exam’s format, from the full prompt to a score on every part.
1
Read the full question
The scenario, its figures, and all three parts, A through C, laid out the way the exam shows them.
2
Write on an 18-minute timer
Inside the 15 to 20 minutes the exam suggests for this question. Pause it or turn it off, and your response saves as you go.
3
Submit for a score out of 8
Your response is scored against the scoring guidelines written for that question. Your first score is included.
Feedback on every part
A summary at the top tells you what to work on next. Below it, each part shows whether you earned the point and what the scoring guidelines were looking for.
Earned the point. You correctly indicated that v₁ > v₂.
Part A: 0/1 point
Did not earn the point. The prompt required justifying in terms of ALL forces that do work. While you discussed the applied force and friction, you failed to mention that the work done by gravity is also the same in both scenarios (or that friction is the only force that changes).
Part A: 1/1 point
Earned the point. You correctly reasoned that the higher coefficient of friction in Scenario 2 leads to a larger friction force, which does more negative work, resulting in a lower final speed.
Detailed feedback on a practice Qualitative/Quantitative FRQ
Questions about the Qualitative/Quantitative FRQ
How many responses can I get scored?
You can read every question without a plan. Your first scored response is included. A plan unlocks unlimited scoring.
Can I use equations in part A?
Part A asks you to justify your claim with physics reasoning, not just an equation. Explain which physical quantities matter and how they change. Part B is where you derive.
How is the QQT different from the Mathematical Routines question?
The QQT starts with reasoning in words, then checks it against a derivation, and is worth 8 points. The Mathematical Routines question adds a graph and is worth 10.
How do I type equations and symbols?
Use the subscript, superscript, and special-character buttons in the editor toolbar. Or write your derivation on paper, switch to handwrite, and add a photo.
Are these real College Board questions?
No. We wrote them in the AP format, with the same three parts, and wrote scoring guidelines for each one.
More AP Physics 1 practice
Mathematical Routines FRQ practice
Mathematical Routines questions with the full scenario, figures, and both parts.
