A plane flying horizontally at an altitude of 3 mi and a speed of 530 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station. {image} mi/h 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Two cars start moving from the same point Two cars start moving from the same point. One travels south at 25 mi/h and the other travels west at 55 mi/h. At what rate is the distance between the cars increasing 4 hours later? Round the result to the nearest hundredth. 61.43 mi/h 60.42 mi/h 60.45 mi/h 58.42 mi/h 60.52 mi/h 60.41 mi/h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A baseball diamond is a square with side 90 ft A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 29 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth if necessary. {image} {image} 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 2 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s how fast is the boat approaching the dock when it is 9 m from the dock? Round the result to the nearest hundredth if necessary. {image} 1 m/s 1.03 m/s 2.02 m/s 1.13 m/s 1.02 m/s 0.97 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2.32 cm/min 1.25 cm/min 2.37 cm/min 12.42 cm/min 2.42 cm/min A water trough is 15 m long and a cross-section has the shape of an isosceles trapezoid that is 35 cm wide at the bottom, 65 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.2 {image} , how fast is the water level rising when the water is 45 cm deep? Round the result to the nearest hundredth. 2.32 cm/min 1.25 cm/min 2.37 cm/min 12.42 cm/min 2.42 cm/min 2.12 cm/min 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

0.35 {image} 1.15 {image} -1.95 {image} 5.05 {image} -0.95 {image} Two sides of a triangle are 5 m and 4 m in length and the angle between them is increasing at a rate of 0.01 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is {image} . 0.35 {image} 1.15 {image} -1.95 {image} 5.05 {image} -0.95 {image} 0.05 {image} 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

165.502 {image} /min 165.845 {image} /min 167.082 {image} /min Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure and volume satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 650 cm {image} , the pressure is 145 kPa, and the pressure is increasing at a rate of 37 kPa/min. At what rate is the volume decreasing at this instant? Round the result to the nearest thousandth if necessary. 165.502 {image} /min 165.845 {image} /min 167.082 {image} /min 165.862 {image} /min 165.972 {image} /min 165.889 {image} /min 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If two resistors with resistances {image} and {image} are connected in parallel, as in the figure, then the total resistance R measured in ohms ( {image} ), is given by {image} . If {image} and {image} are increasing at rates of 0.6 {image} / s and 0.7 {image} / s respectively, how fast is R changing when {image} and {image} ? Round the result to the nearest thousandth if necessary. {image} 0.327 {image} /s 0.389 {image} /s 0.366 {image} /s 1.417 {image} /s 0.44 {image} /s 0.38 {image} /s 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

0.143 rad/s 0.166 rad/s 0.205 rad/s 0.132 rad/s 1.173 rad/s A television camera is positioned 3,300 ft from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its speed is 680 ft/s when it has risen 2,200 ft. If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at this moment? Round the result to the nearest thousandth if necessary. 0.143 rad/s 0.166 rad/s 0.205 rad/s 0.132 rad/s 1.173 rad/s 0.313 rad/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A runner sprints around a circular track of radius 160 m at a constant speed of 3 m/s. The runner's friend is standing at a distance 280 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 280 m? Round the result to the nearest thousandth if necessary. 2.903 m/s 4.085 m/s 2.823 m/s 2.875 m/s 2.985 m/s 2.828 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50