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Take the quiz when ready: https://1drv.ms/w/c/2713457aa143ce7f/... Kinematics Problems II | Dropping a Package While Ascending + Max Height of a Bullet | Full Step‑By‑Step Solutions In this lesson from the MathSupport channel, @mathsupportnow , we solve two challenging kinematics problems involving vertical motion, initial upward velocity, gravity, and quadratic equations. These examples go beyond the basics and show how to correctly apply the Big Five equations when objects are moving upward before falling, or when they reach maximum height in projectile motion. Every step is broken down clearly so you can master the reasoning behind each calculation. ✅ What You’ll Learn in This Video 🔹 Problem 1 — Dropping a Package from an Ascending Helicopter Understanding why the initial velocity is upward Setting displacement as negative when falling to the ground using a formula for d Recognizi.ng when the equation becomes quadratic Solving for time using the quadratic formula Why the negative root must be rejected Final result: package reaches the ground in 5.83 s 🔹 Problem 2 — Bullet Fired Straight Up Using V ^2 to find maximum height Why 𝑣𝑓 = 0 at the top of the trajectory Computing the bullet’s peak height: 1,690 m (≈1.7 km) Finding time to reach the top Using symmetry of motion to find total time in the air Understanding why acceleration is never zero during the entire flight (gravity acts at all times) 00:00 – Introduction: Two advanced kinematics problems 00:08 – Problem 1 setup: Helicopter ascending + package dropped 00:36 – Identifying initial velocity, displacement, and acceleration 01:32 – Using the displacement equation 02:13 – Why this becomes a quadratic equation 03:14 – Quadratic formula setup 04:46 – Choosing the correct (positive) root 05:41 – Common mistake: misunderstanding initial velocity 07:08 – Problem 2 setup: Bullet fired straight up 07:50 – Using Vf^2 to find max height 09:07 – Time to reach the top 10:32 – Total time in the air 11:19 – Trick question: When is acceleration zero? (Never) 12:22 – Final reminders & quiz link This video is ideal for: 🎯 Science 10 🎯 Physics 11 (Kinematics Unit) 🎯 AP Physics 1 Foundations 🎯 Students preparing for quizzes, tests, or final exams 🎯 Teachers and tutors needing clear worked examples 👍 Like if this helped you 🔔 Subscribe for more step‑by‑step physics tutorials 💬 Comment with your questions or requests 📤 Share with classmates or study groups #Kinematics #ProjectileMotion #VerticalMotion #Physics11 #Science10 #QuadraticFormula #Mathsupport #BigFiveEquations