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17 related rates problems.notebook
1
October 20, 2008
Oct 1410:18 AM
Related Rates Problems
![Page 2: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/2.jpg)
17 related rates problems.notebook
2
October 20, 2008
Oct 1412:16 PM
The width of a rectangle is 10 cm more than three times the height. The height is changing at the constant rate of 1.5 cm/sec. Find the rate at which the area is changing at the instant the height is 15 cm.
![Page 3: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/3.jpg)
17 related rates problems.notebook
3
October 20, 2008
Oct 1412:23 PM
The height of a right triangle is three times the width. The width of the triangle is decreasing at the rate of 2 cm/sec. Calculate the rate at which the height is decreasing at the instant the width is 25 cm.
![Page 4: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/4.jpg)
17 related rates problems.notebook
4
October 20, 2008
Oct 1412:26 PM
The height of a cylinder is always four times the radius. The radius is increasing at the rate of 3 cm/sec. Calculate the rate at which the volume is increasing at the instant the volume is 800 cc.
![Page 5: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/5.jpg)
17 related rates problems.notebook
5
October 20, 2008
Oct 1412:27 PM
The height of a cylinder is increasing at the rate of 2 cm/sec while the radius is decreasing at the rate of 3 cm/sec. Find the rate at which the volume is changing at the instant the radius is 200 cm and the height is 800 cm.
![Page 6: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/6.jpg)
17 related rates problems.notebook
6
October 20, 2008
Oct 1412:29 PM
A cube is expanding in such a way that its edge is changing at the rate of 3 m/sec. When its edge is 6 m long, find the rate of change in the volume.
![Page 7: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/7.jpg)
17 related rates problems.notebook
7
October 20, 2008
Oct 1412:30 PM
A spherical snowball is melting so that the radius is decreasing at the rate of 0.4 cm/sec . When the radius is 6 cm , find the rate of change of the volume.
![Page 8: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/8.jpg)
17 related rates problems.notebook
8
October 20, 2008
Oct 1412:31 PM
The volume of a spherical snowball is decreasing at the rate of 0.8 cc/sec. What is the rate of change of the radius when the radius has been reduced to 5 cm?
![Page 9: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/9.jpg)
17 related rates problems.notebook
9
October 20, 2008
Oct 1412:32 PM
A right angled triangle is four times as high as is the base. Find the rate of change of the area when the base has shrunk to 12 cm at a rate of 2 cm/sec.
![Page 10: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/10.jpg)
17 related rates problems.notebook
10
October 20, 2008
Oct 1412:33 PM
The side of an equilateral triangle increases at the rate of 3 cm/sec. At what rate is the area increasing when the sides are 12 cm long?
![Page 11: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/11.jpg)
17 related rates problems.notebook
11
October 20, 2008
Oct 1412:35 PM
A water tank shaped like a cone has height 6 m and diameter 8 m at the top.
a) Suppose water enters at the rate 2 cu m/min . Find the rate at which the water level is rising at the instant the water is 1 m deep.
![Page 12: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/12.jpg)
17 related rates problems.notebook
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October 20, 2008
Oct 1412:37 PM
b) Suppose the water is leaving the tank. The height is dropping at the rate 0.6 m/sec. Find the rate of decrease of the volume when the radius is 2 m.
![Page 13: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/13.jpg)
17 related rates problems.notebook
13
October 20, 2008
Oct 1412:38 PM
A spotlight on the ground shines on a wall 10 m away. A man 2 m tall walks from the spotlight toward the wall at a speed of 1.2 m/sec. How fast is his shadow on the wall decreasing when he is 3 m from the wall?
![Page 14: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/14.jpg)
17 related rates problems.notebook
14
October 20, 2008
Oct 1412:40 PM
A man starts walking north at a speed of 1.5 m/sec. and a woman starts at the same time from the same point walking west at a speed of 2 m/sec. At what rate is the distance between them changing 2 minutes later?
![Page 15: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/15.jpg)
17 related rates problems.notebook
15
October 20, 2008
Oct 1412:41 PM
Two ships start at the same point at 12 noon. One ship travels east at 5 km/hr and the other north at 7 km/hr. Find the speed of separation at 3 PM.
![Page 16: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/16.jpg)
17 related rates problems.notebook
16
October 20, 2008
Oct 1412:42 PM
Ship A is 6 km east of ship B at 12 noon. Ship A sails east at 4 km/hr and ship B south at 3 km/hr. Find the speed of separation at 2 PM.
![Page 17: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/17.jpg)
17 related rates problems.notebook
17
October 20, 2008
Oct 1412:43 PM
At 12 noon ship A is 2 km north of a port while ship B is 10 km east of the same port. Ship A is travelling norht at 3 km/hr while ship B is travelling west at 4 km/hr. Find the rate of separation of the two ships at 2 PM.
![Page 18: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/18.jpg)
17 related rates problems.notebook
18
October 20, 2008
Oct 1412:44 PM
A rocket is launched vertically and is tracked by a radar station , which is located on the ground 3 miles from the launch site. What is the vertical speed of the rocket at the instant when its distance from the radar station is 5 miles and the distance is increasing at the rate of 5000 miles/hr?
![Page 19: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/19.jpg)
17 related rates problems.notebook
19
October 20, 2008
Oct 141:31 PM
A man 6 ft tall walks with a speed of 8 ft/sec away from a street light on top of an 18 ft pole. How fast is the tip of his shadow moving along the ground when he is 100 ft from the light pole?
![Page 20: 17 related rates problems.notebook - CBEprojects.cbe.ab.ca/Aberhart/jkotow/math31/diffrrprob.pdf · 17 related rates problems.notebook 3 October 20, 2008 Oct 1412:23 PM The height](https://reader031.vdocument.in/reader031/viewer/2022021822/5b14c76b7f8b9a4e2c8bcfff/html5/thumbnails/20.jpg)
17 related rates problems.notebook
20
October 20, 2008
Oct 141:33 PM
A man 6 ft tall walks with a speed of 8 ft/sec away from a street light on top of an 18 ft pole. How fast is LENGTH of his shadow along the ground changing when he is 100 ft from the light pole?