Uploaded April 2026 | Updated September 2026, 1 week ago

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A useful resource for students preparing for MCV4U, IB, and AP Calculus.
👉 Get it here: amazon.com/dp/1069386243
A rope passes over a pulley that is 5 m above the ground.
One end is attached to a box, and the other is tied to a truck moving horizontally away from the pulley at a constant speed of 0.5" m/s" .
The attachment point on the truck is 1 m above the ground.
Find the rate at which the box is rising when the truck is 3 m from the plumb line.

🔍 READ • TRANSLATE • PLAN
Given:
dx/dt=0.5" m/s"

Find:
dy/dt "at " x=3

Key Observation:
Vertical difference between pulley and truck attachment:
5-1=4

🧠 CORE IDEA (Highlight Box)
👉 Right Triangle Relationship
z^2=x^2+4^2

⚙️ SOLUTION (Step-by-Step, Compact)
Step 1: Differentiate
2z dz/dt=2x dx/dt
dz/dt=x/z⋅dx/dt


Step 2: Evaluate at x=3
z=√(3^2+4^2 )=5
dz/dt=3/5⋅0.5=0.3


Step 3: Rope Length Relation
L=z+5-y

Differentiate:
0=dz/dt-dy/dt
dy/dt=dz/dt

✅ FINAL ANSWER (Bold Box)
▭(dy/dt=0.3" m/s" )

The box is rising at 0.3 m/s.

📌 Perfect for:
AP Calculus students
IB Mathematics learners
High school and early university students
Anyone building strong calculus fundamentals
youtube.com/@MathematicsTutor For Guidance Contact : anil.anilkhandelwal@gmail.com
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