Parkour Path Logic

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What this quiz asks

1. A traceur jumps from a ledge and lands at a position represented by vector A = (3, 4) meters. If their next jump is represented by vector B = (2, 1) meters, what is the total displacement vector from the starting point?
2. A parkour athlete moves along a wall with displacement vector V₁ = (6, -2) m. They then change direction with vector V₂ = (-4, 5) m. What is the net displacement vector?
3. A parkour jump path is defined by vector P = (10, 8) m. If the athlete realizes they overshot and needs to adjust by vector A = (-3, -2) m, what is the final corrected displacement vector?
4. A parkour route consists of three segments: V₁ = (2, 5), V₂ = (4, -1), and V₃ = (-1, 2). What is the resultant displacement vector for the entire route?
5. To land a jump safely on a flat surface, the angle of impact θ must be minimized. If your trajectory angle is 30° relative to the horizontal, what is the landing angle relative to the vertical surface?
6. If a traceur approaches a ledge and their landing force vector is split into horizontal (x) and vertical (y) components where x=4 and y=3, what is the resultant impact angle θ? Use tan(θ) = y/x.
7. To optimize landing, you need to land such that the impact angle is within the 'safe zone' defined by 20° ≤ θ ≤ 40°. Which of the following calculated landing angles are safe?
8. You are jumping from a height where your landing velocity v_y is 5 m/s and your horizontal velocity v_x is 5 m/s. What is the impact angle θ? Note: θ = arctan(v_y / v_x).
9. A traceur weighs 60 kg and moves at 4 m/s. What is their momentum (p = mv)?
10. If a parkour athlete increases their velocity from 2 m/s to 6 m/s while maintaining a constant mass, how does the momentum ratio change?
11. Two athletes have a momentum ratio of 1:2. If athlete A has mass 50 kg and velocity 4 m/s, what is athlete B's momentum?
12. To maintain a constant momentum of 300 kg·m/s, if an athlete's mass increases from 60 kg to 75 kg, what must their new velocity be?
13. A traceur faces a decision tree with 3 starting paths. Path A leads to 2 sub-paths, Path B leads to 3, and Path C leads to 1. How many total potential route endings exist?
14. A parkour course has a binary decision tree. Each decision point splits into 2 choices. If the route lasts for 4 consecutive decisions, how many possible paths exist?
15. A route has 3 stages. Stage 1 has 3 options, Stage 2 has 2 options, and Stage 3 has 4 options. How many total unique paths can be formed?
16. A route planner blocks 2 of the 10 available paths in a 3-level tree where each level doubles choices. If 16 paths existed originally, how many remain?
17. A parkour athlete has a 70% probability of landing a specific jump successfully. If they attempt this jump 3 times in a row, what is the probability that all 3 jumps are successful?
18. An athlete chooses between two routes. Route A has a 20% risk of injury, and Route B has a 1/6 risk of injury. Which route is statistically safer?
19. If the probability of failing a vault is 0.15, what is the probability of failing at least once in 2 attempts?
20. An athlete faces a jump where the probability of success is 'p'. If the probability of success over 2 attempts is 0.64, what is 'p'?
21. A traceur weighs 60 kg and runs at 5 m/s. Calculate their kinetic energy using KE = 0.5 × m × v². What is the total kinetic energy in Joules?
22. If a parkour athlete doubles their velocity from 4 m/s to 8 m/s, by what factor does their kinetic energy increase? Use KE = 0.5 × m × v².
23. A traceur performs a jump requiring 1200 J of energy. If they have 800 J of kinetic energy and 500 J of potential energy stored, do they succeed?
24. Find the velocity required to achieve 2000 J of energy for a 40 kg mass. Use v = √(2 × KE / m).

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