Welcome to Clip from Spiral logo

Interactive video lesson plan for: related rates boat and winch Derivatives calculus differentiation Optimization

Activity overview:

Subscribe Here
For more cool math videos visit our site at or


#1 Circles Oil is dropping from a punctured tank onto a circular oil pool on the ground with radius r. Find the following and state their meanings and units.
a) dr/dt
c) How fast is the radius changing when the radius is 2 cm and the area is changing at 20p cm2/min

#2 Cones:A conical pit is being filled with concrete. The pit has a base radius of 10 cm, and a depth of 30 cm. The pit is being filled so that the height of water rises at 2 cm/sec. Find the following in terms of V and h, (include meaning & units).
a) dh/dt
c) How fast is pit being filled at the point in time that the water level is 4cm.

#3 Spheres A sphere being inflated at 10ft^3/sec How fast is the radius increasing once the radiums is 4ft ?
#4 Ladder: A ladder 13 ft long is sliding down a wall. At the moment the base is 12ft from the wall, the base of the ladder is moving at 5 ft/sec. How fast is the top of the ladder moving at this moment?

#5 Boat and Winch: A winch 20 feet above sea level is used to reel in a rope connected to a boat at 2 ft/sec. How fast is the boat moving when the rope is 45 feet in length.

Ice Cube: An ice cube melts uniformly at a rate of 27cm3/sec. If the cube retains its perfect form while it is melting, at what rate are the sides shrinking when each side is 3 cm long ?

#Inverted conical Tank: water runs out of a conical tank at 7ft^3/min. The tank has a base of 10ft and a depth of 12 ft. How fast is the water level rising when the water is 5ft deep

#7 Trapezoidal Trough:The ends of a horizontal water trough is an isoceles trapezoidal prism. The length is 8 feet and the lower base is 4 feet. The upper base is 10 feet and the depth of the trough is 2 feet. If the water level is rising at 3 feet/min, when the depth of the water is 1 foot, how fast is water being poured into the trough?

#9 Hot air Balloon:A hot air balloon is rising vertically from a level platform. A range finder 400 feet from the lift point is tracking the hot air balloon. At the moment the angle of elevation of the range finder is 60 degrees , the angle of elevation is increasing at .10 degrees/minute. How fast is the balloon rising at that moment?

Consider a sphere of radius 10cm.
If the radius changes 0.1cm (a very small amount) how much does the volume change?
Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping?
Truck A travels east at 40 mi/hr.
Truck B travels north at 30 mi/hr.
How fast is the distance between the trucks changing 6 minutes later?

A particle moves along the curve C ú »" Ä B fi As it reaches $
the pointa b #fl $ fl the y-coordinate is increasing at a rate of
4 cm/sec. How fast is the x-coordinate of the point changing
at this instant?
3. Suppose where is a constant and when

4. Two cars start moving from the same point. One travels south at
60 m/hr and the other travels west at 25 m/hr. At what rate is
the distance between the cars increasing two hours later?
5. A plane flying horizontally at an altitude of 1 mile and a speed
of 500 mph passes over a radar station. Find the rate at which
the distance from the plane to the station is increasing when it
is 2 miles away from the station.
6. A conical water tower has a height of 12 ft and a radius of 3 ft.
Water is pumped into the tank at a rate of 4 ft /min. How fast is $
the water level rising when the water level is 6 ft

A man walks along a straight path at a speed of 4 ft/s.
A searchlight is located on the ground 20 ft from the path and is kept focused on the man.
§At what rate is the searchlight rotating
when the man is 15 ft from the point on
the path closest to the searchlight?
A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding
car that has turned the corner and is now moving straight east. When the cruiser is 0.6
mi north of the intersection and the car is 0.8 mi to the east, the police determine with radar
that the distance between them and the car is increasing at 20 mph. If the cruiser is moving
at 60 mph at the instant of measurement, what is the speed of the car?
The voltage V (volts), current I (amperes),
and resistance R (ohms) of an electric circuit like the one shown
here are related by the equation V IR. Suppose that V is
increasing at the rate of 1 volt sec while I is decreasing at the
rate of 13 ampsec. Let t denote time in sec.
A trough is 15 ft long and 4 ft across the top
as shown in the figure. Its ends are isosceles triangles with
height 3 ft. Water runs into the trough at the rate of 2.5 ft3min.
How fast is the water level rising when it is 2 ft deep?
Sliding Ladder A 13-ft ladder is leaning against a house (see
figure) when its base starts to slide away. By the time the base is
12 ft from the house, the base is moving at the rate of 5 ft sec.

Tagged under: Maximum,increasing,Minimum,global,volume,point inflection,area,patrickJMT fencing,Khan Academy box,related rates cone,conical,open,prism,primary,trough,secondary,sphere,endpoints,critical points,circular,applicaton,distance,moment,point,searchlight,inscribed,rate,cone,rising,falling,surface,ladder,absolute,boat,antiderivative,tank,concave ,concace ,pythagorean,curve,similar,shadow,geometry,tall,altitude changing

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share related rates boat and winch Derivatives calculus differentiation Optimization on Google+ Share related rates boat and winch Derivatives calculus differentiation Optimization on Twitter Share related rates boat and winch Derivatives calculus differentiation Optimization on Facebook Pin related rates boat and winch Derivatives calculus differentiation Optimization Email related rates boat and winch Derivatives calculus differentiation Optimization

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.


Carry out a quickfire formative assessment to see what the whole class is thinking


Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices


Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome