related rates
A child is flying a kite at a constant 120 ft altitude. If the child lets the kite string out at a constant rate of 2.5 ft/sec, how fast is the kite moving when 130 ft of string has been let out?
Oil is spilling from a damaged tanker onto the large lake surface. The oil makes a circular film (1 cm thick). If the oil is flowing at a rate of 15m^3 per minute, how fast is the radius of the oil slick increasing after 30 minutes?
A large steel cylinder is standing upright. The volume of the cylinder remains constant (stays a cylinder) as its pressed down upon by a heavy weight. If the cylinder initially has a height of 4 cm and 1 cm for the radius, how fast is the radius of the cylinder when the height has been cut in half of and is decreasing at a rate of 0.2 cm/min.
Homework Answers
Oil Spill In calm waters, the oil spilling from the ruptured hull of a grounded tanker...
Oil Spill In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. If the radius r of the circle is increasing at the rate of re) - Vat+9 ft/mint min after the rupture occurs, find an expression for the radius at any time. Hint: (0) - 0. How large is the polluted area 36 min after the rupture occurred?
Question No: 5 Marks: 3+3+3 +4 a) Assume that oil spilled from a ruptured tanker spreads...
Question No: 5 Marks: 3+3+3 +4 a) Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 6 ft/s. i) Find the rate at which the circumference is increasing ii) How fast is the area of the spill increasing when the radius of the spill is 30 ft? b) The three different balls are thrown vertically upwards from the top of a building, the following functions express the height...
Explanantion for 7 and 8. 8 An inverted conical tank has height 4 m and radius...
Explanantion for 7 and 8.
8 An inverted conical tank has height 4 m and radius 1 m at the top. When the d oil flows in at the rate 2 m/min. How fast is the level rising? 9 A 6-ft man walks away from a 15-ft lamp post. When he is 21 ft from the post.
Answers are written in, please explain step process on how to achieve answers. 3. An open-top...
Answers are written in, please
explain step process on how to achieve answers.
3. An open-top cylindrical container of radius R 100 cm is initially filled up with water of height hi = 1 .30 m, and a layer of oil (insoluble to water) of height h, = 0.85 m on top of the water. The density of oil is 0.75 times of the density of water. A faucet of diameter 1.20 cm has been punched near the bottom of...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need...
2) Find the area of the region enclosed by each group of equations. a) y x, y sin x, b) y x2-2x, y= x+ 4 x 3) A part...
2) Find the area of the region enclosed by each group of equations. a) y x, y sin x, b) y x2-2x, y= x+ 4 x 3) A particle moves along a straight line with a velocity of 5 cm/s and then accelerates at a rate of a(t) t2+2. What is its displacement after 5 seconds of acceleration (acceleration is in cm/s2) 4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially...
4. A tank is filled with incompressible oil to a depth of (h) 6.43 m open...
4. A tank is filled with incompressible oil to a depth of (h) 6.43 m open tank The tank is being drained via a horizontal pipe that is attached at a height of (h2) 0.789 m above the tank bottom. Oil is flowing out of the tank into the pipe at a rate of 2.34 x 10 m'/s, but the tank is so large that the descent speed of the oil level at the top is negligible (0) The gauge...
A tank is filled with incompressible oil to a depth of (h_1) 6.43 m. The tank...
A tank is filled with incompressible oil to a depth of (h_1) 6.43 m. The tank is being drained via a horizontal pipe (radius 1.92 cm), attached at a height of (h-2) 0.789 m above the tank bottom. Oil is flowing out through the pipe at a rate of 2.34 times 10^-3 m^3/s, but the tank is so large that the descent speed of the oil level at the top is negligible (almostequalto 0). The gauge pressure in the drain...
A U-tube contains liquid of unknown density. An oil of density 770 kg/m³ is poured into...
A U-tube contains liquid of unknown density. An oil of density
770 kg/m³ is poured into one arm of the tube until the oil column
is 13.5 cm high. The oil-air interface is then 4.5 cm above the
liquid level in the other arm of the U-tube. Find the density of
the liquid.
A raft is made of 11 logs lashed together. Each is 38.0 cm in
diameter and has a length of 7.00 m. How many people (whole number)...
4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially empty a...
4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially empty and rain enters the can during a 60-day period. The height of water in the can is modeled by the function S, where S(t) is measured in millimeters and t is measured in days for 0sts 60. The rate at which the height of water is rising in the can is given by S'(t) = 2 sin(0.03t) of the 60-day period?...
Oil Spill In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. If the radius r of the circle is increasing at the rate of re) - Vat+9 ft/mint min after the rupture occurs, find an expression for the radius at any time. Hint: (0) - 0. How large is the polluted area 36 min after the rupture occurred?
Question No: 5 Marks: 3+3+3 +4 a) Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 6 ft/s. i) Find the rate at which the circumference is increasing ii) How fast is the area of the spill increasing when the radius of the spill is 30 ft? b) The three different balls are thrown vertically upwards from the top of a building, the following functions express the height...
Explanantion for 7 and 8.
8 An inverted conical tank has height 4 m and radius 1 m at the top. When the d oil flows in at the rate 2 m/min. How fast is the level rising? 9 A 6-ft man walks away from a 15-ft lamp post. When he is 21 ft from the post.
Answers are written in, please
explain step process on how to achieve answers.
3. An open-top cylindrical container of radius R 100 cm is initially filled up with water of height hi = 1 .30 m, and a layer of oil (insoluble to water) of height h, = 0.85 m on top of the water. The density of oil is 0.75 times of the density of water. A faucet of diameter 1.20 cm has been punched near the bottom of...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need...
2) Find the area of the region enclosed by each group of equations. a) y x, y sin x, b) y x2-2x, y= x+ 4 x 3) A particle moves along a straight line with a velocity of 5 cm/s and then accelerates at a rate of a(t) t2+2. What is its displacement after 5 seconds of acceleration (acceleration is in cm/s2) 4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially...
4. A tank is filled with incompressible oil to a depth of (h) 6.43 m open tank The tank is being drained via a horizontal pipe that is attached at a height of (h2) 0.789 m above the tank bottom. Oil is flowing out of the tank into the pipe at a rate of 2.34 x 10 m'/s, but the tank is so large that the descent speed of the oil level at the top is negligible (0) The gauge...
A tank is filled with incompressible oil to a depth of (h_1) 6.43 m. The tank is being drained via a horizontal pipe (radius 1.92 cm), attached at a height of (h-2) 0.789 m above the tank bottom. Oil is flowing out through the pipe at a rate of 2.34 times 10^-3 m^3/s, but the tank is so large that the descent speed of the oil level at the top is negligible (almostequalto 0). The gauge pressure in the drain...
A U-tube contains liquid of unknown density. An oil of density
770 kg/m³ is poured into one arm of the tube until the oil column
is 13.5 cm high. The oil-air interface is then 4.5 cm above the
liquid level in the other arm of the U-tube. Find the density of
the liquid.
A raft is made of 11 logs lashed together. Each is 38.0 cm in
diameter and has a length of 7.00 m. How many people (whole number)...
4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially empty and rain enters the can during a 60-day period. The height of water in the can is modeled by the function S, where S(t) is measured in millimeters and t is measured in days for 0sts 60. The rate at which the height of water is rising in the can is given by S'(t) = 2 sin(0.03t) of the 60-day period?...
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