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17 related rates problems.notebook
1
October 20, 2008
Oct 1410:18 AM
Related Rates Problems
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.
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.
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.
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.
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.
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.
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?
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.
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?
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.
17 related rates problems.notebook
12
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.
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?
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?
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.
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.
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.
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?
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?
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?
