# An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation tetra is changing when the

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1. ## Calculus

An airplane flys at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when

2. ## Geometry

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home,

3. ## Physics

An airplane flies 220 km due east, makes a right-angle, and then flies 400 km due north. Find the magnitude of the plane's displacement from it's starting point. Neglect the culrvature of the earth

4. ## Physics

"An airplane is climbing at an angle of 15 degrees to the horizontal with the sun directly overhead. The shadow of the airplane is observed to be moving across the ground at 200 km/h. How long does it take for the plane to increase its altitude by 1000 m"?

5. ## Trigonometry

An airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation as 11˚ and 20˚. How high is the airplane? Round to the nearest hundredth of a mile.

6. ## Calculus

An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation tetra is changing when the angle is 30 degrees

7. ## math

An airplane flies from Ft. Myers to Sarasota, a distance of 150 miles, and then turns through an angle of 50° and flies to Orlando, a distance of 100 miles (see the figure). (a) How far is it from Ft. Myers to Orlando? (b) Through what angle should the

8. ## Calculus-rates

1.) A man 6 ft tall walks at a rate of 5 ft per sec. from a light that is 15 ft above the ground. At what rate is the top of his shadow changing? 2.) An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the

9. ## Calculus

An airplane flies at an altitude of y = 5 miles toward a point directly over an observer (see figure). The speed of the plane is 500 miles per hour. Find the rates at which the angle of elevation 𝜃 is changing when the angle is 𝜃 = 45°, 𝜃 = 60°,

10. ## math

An airplane leaves Atlanta at 2 PM and flies north at 250 miles per hour. A second airplane leaves Atlanta 30 minutes later and flies north at 280 miles per hour. At what time will the second airplane overtake the first? Answer Choices 6:20 PM 6:00 PM 6:40

11. ## algebra

An airplane flies 750 miles due west in 1 1/2 hours and 750 miles due south in 2 hours. What is the average speed of the airplane?

12. ## PRECALCULUS

An airplane is flying at a speed of 250 mph at an altitude of 4 miles. The plane passes directly above a radar station at time t=0. Find the distance s between the plane and the radar station after 5 minutes.

13. ## Math Trigonometry

A plane flies in a direction of 85° from Chicago. It then turns and flies in the direction of 200° for 150 miles. It is then 195 miles from its starting point. How far did the plane fly in the direction of 85°? I am confused about aereal navigation. Can

14. ## math

A model airplane flies 18 feet in 2 seconds. what is the airplane's speed in miles per hour? round your answer to nearest hundredth.

an airplane's altitude is 100 feet as it descents for a landing on a runway whose touchdown is 5000 ft away. Let the x-axis represent the ground and the y-axis represent the airplane's altitude. What is the slope of the airplane's descent? What is the

16. ## Algebra

An airplane flies 165 miles from point A in the direction 130 degrees and then travels in the direction 245 degrees for 80 miles. Approximately how far is the airplane from A?

17. ## Calculus

An airplane flies at an altitude of y = 5 miles toward a point directly over an observer. The speed of the plane is 500 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is θ = 45°, θ = 60°, and θ = 80°.

18. ## trig

Two Airplanes leave an airport at the same time on different runways. One flies on a bearing of N66degreesW at 325 miles per hour. The other airplane flies on a bearing öf S26degreesW at 300 miles per hour. How far apart will the airplanes be after 2

19. ## Calculus

A rocket is fired vertically into the air at the rate of 6 miles/min. An observer on the ground is located 4 miles from the launching pad. When the rocket is 3 miles high, how fast is the angle of elevation between the rocket and the observer changing?

20. ## algebra 1

a model airplane flies 18 feet in 2 seconds. What is the airplane's speed in miles per hour?

21. ## modern physics

a hunter on the ground fires a bullet in the northeast direction which strikes a deer 0.25 metre away from him, the bullet travel with a speed of 1800m/hr.at the instant an airplane is directly over the hunter at an altitude of one metre and is traveling

22. ## Physics

The pilot of a small plane finds that the airport where he intended to land is fogged in. He flies 55 miles west to another airport to find that conditions there are too icy for him to land. He flies 25 miles at 15 degrees east of south and is finally able

23. ## calculus

An airplane flys at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when

24. ## Math

An airplane flys at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when

25. ## Math

An airplane is flying at an altitude of 6 miles and passes directly over a radar antenna. When the plane is 10 miles away, the radar detects that the distance is changing at a rate of 240 mph. what is the speed of the plane? This is an implicit

26. ## math help pls

Two observers who are 5 km apart simultaneously sight a small airplane flying between them. One observer measures a 51.0-degree inclination angle, while the other observer measures a 40.5-degree inclination angle. At what altitude is the airplane flying?

27. ## trigonometry

The angles of elevation to an airplane from two points A and B on level ground are 50◦ and 67◦ , respectively. The points A and B are 3.9 miles apart, and the airplane is east of both points in the same vertical plane. Find the altitude of the plane.

28. ## SOMEONE HELP PLEASE..DUE AT MIDNIGHT

Hot dogs and Hamburgers: 1.) The caterer for your class picnic charges \$1 for each hotdog and \$2 for each hamburger. You have \$48 to spend. Write a model that shows the different numbers of hot dogs and hamburgers that you could purchase... 2.) Airplane

29. ## Trig

Two observers 1 km apart spot an airplane. The angles of elevation of the airplane from the two observers are 22 degrees 50 minutes and 24 degrees 40 minutes. If the observers and the airplane are in the some vertical plnae, compute the altitude of the

30. ## calculus

An airplane flying west at 300 miles per hour goes over the control tower at noon, and a second airplane at the same altitude, flying north at 400 miles per hour, goes over the tower an hour later. How fast is the distance between the airplanes changing at

31. ## Calculus

Derivatives - chain rule An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint:

32. ## calculus

an airplane is flying at an altitude of 6.7 miles towards a point directly over an observer. if the speed of the plane is 499 miles per hour, find the rate at which the angle of observation, Ɵ, changing by at the moment when the angle is 21 degrees.

33. ## calculus

Please answer. An airplane at an altitude of 3000m, flying horizontally at 300km/hr, passes directly over an observer. Find the rate at which it is approaching the observer when it is 5000m away.

34. ## algebra

an airplane flies with a constant speed of 500 miles per hour. How long will it take to travel a distance of 1500 miles

35. ## geometry

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home,

36. ## geometry

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home,

37. ## Math- Geometry

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home,

38. ## Pre cal

1. An airplane flies 200 km on course 110 degrees from point A to point B. At point B the pilot changes course to 37 degrees. The plane then flies 100 km to point C. Find the magnitude of the net displacement from A to C. 2. A plane is flying on a bearing

39. ## Math

An airplane in Australia is flying at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of

40. ## Math/Trig

An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction 210°50'. Assuming the Earth is flat, how far is the plane from the airport at this time (to the nearest mile)

41. ## calculus

An airplane flies at an altitude of 5mies toward a point directly over an observer. The speed of the plain is 600 miles per hour. Find the rate at which the angle of elevation thetha is changing when the angle is 75 degrees. Please help with this question.

42. ## Precalculus

An airplane flies 180 miles from point A in the direction 135° and then travels in the direction 240° for 90 miles. Approximately how far is the airplane from A? (Round your answer to the nearest whole number.)

43. ## math

A search and rescue plane flying at an altitude of 1000 feet spots a ship in the ocean with an angle of depression of 7 degrees. The pilot follows his line of site and flies directly toward the boat for 0.7 miles. At this point his altitude is _____ feet.

44. ## trigonometry HARD!!

An airplane flies due north from a starting point at 234.6 mph for 40 minutes. Then turns flying 20 minutes at 252 mph in the direction N 20 degree 31 minutes East. How many miles is the airplane from the starting point?

45. ## Math, Pre-Calculus.

A postal airplane leaves lsland A and flies 91 miles to Island B. It drops off and picks up mail and flies 63 miles to lsland C. After unloading and loading A- mail, the plane returns to lsland A at an average rate of 300 miles per hour. How long does it

46. ## math

Two observers who are 5 km apart simultaneously sight a small airplane flying between them. One observer measures a 51.0-degree inclination angle, while the other observer measures a 40.5-degree inclination angle. At what altitude is the airplane flying?

47. ## Math. Help Thanks!

Hot dogs and Hamburgers: 1.) The caterer for your class picnic charges \$1 for each hotdog and \$2 for each hamburger. You have \$48 to spend. Write a model that shows the different numbers of hot dogs and hamburgers that you could purchase... 2.) Airplane

48. ## Geometry

an airplane flying at an altitude of 10,000ft or 1.89 miles. The airport at which it is schooled to land is 50 mi away. Find the average angle at which the airplane must descent for landing round your answer to the nearest degree.

49. ## Math

An airplane flies 2,750 miles in 5 hours. Find the unit rate in miles per second. Round the answer to the nearest hundredth. I appreciate the help very much. I got .132 but I think I'm wrong.

50. ## Intermediate Algebra

An airplane ascends 150 feet as it flies a horizontal distance of 1000 feet. How much altitude will it again as it flies a horizontal distance of 1 mile. (hint: 5280=1mile.)

51. ## Pre-Calc

An airplane is flying at a speed of 250 mph at an altitude of 4 miles. The plane passes directly above a radar station at time t = 0. What is the distance s between the plane and the radar station after four minutes?

52. ## Science

An airplane with a speed of 27.4 m/s is climbing upward at an angle of 48° counterclockwise from the positive x axis. When the plane's altitude is 860 m the pilot releases a package. (a) Calculate the distance along the ground, measured from a point

53. ## Math

An airplane leaves the airport and flies due west 170 miles and then 240 miles in the direction 200°30'. Assuming the earth is flat, how far is the plane from the airport at this time( to the nearest mile)?

54. ## Math

An airplane ascends 450 feet at a constant rate as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? (Hint: 5,280 feet = 1 mile.)

55. ## calculous

An airplane flies at an altitude of 2 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°, and θ =

56. ## calculous

An airplane flies at an altitude of 2 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°, and θ =

57. ## Calculus

Derivatives - chain rule An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint:

58. ## calculus

An airplane is cruising at 340 km/h at an altitude of 4000 m. If the plane passes directly over an observer on the ground, how fast is the distance from the plane to the observer changing when it is 3000 m away from the point directly above the observer?

59. ## physics

The velocity of sound in the atmosphere is c=300 m/s. An airplane is traveling with velocity v=600 m/s at an altitude of h=8 km over an observer. How far horizontally past the observer in kilometers will the plane be when the observer first hears the noise

60. ## Calculus

An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 mi/hr. Find the rate at which the angle of elevation is changing when the angle is 30 degrees. I found the answer to be 60 radians/hr by

61. ## Calculus

An airplane is flying above an observer standing on the ground. At the moment it passes overhead, the observer judges by its apparent size that the airplane’s altitude is 30,000 feet. It takes 50 seconds for the plane, moving in a straight, horizontal

62. ## Physics

An airplane is flying above an observer standing on the ground. At the moment it passes overhead, the observer judges by its apparent size that the airplane’s altitude is 30,000 feet. It takes 50 seconds for the plane, moving in a straight, horizontal

63. ## Math

An observer at point 0 sees airplane P directly over airport a. The observer measures the angle of the plane at 40.5. Find m

64. ## Trig

An airplane flies 180 miles from point A in the direction 120 degrees and then travels 210 degrees for 80 miles. Approximately how far is the airplane from point A? I know that I will need to use the law of cosine. distance^2= a^2+b^2-2abcos? I am not sure

65. ## Math

At an airport, a flight controller is in a tower 45m above the ground. She observes an airplane flying at a constant altitude at an angle of elevation of 14 degrees from her line of sight. Seven seconds later, the airplane flies directly overhead. If the

66. ## Physical Science

an airplane is flying at 600km/h at an altitude of 2.0km. When the sound of the airplane's engines seems to someone on the ground to be coming from directly overhead, how far away is she from being directly below the airplane?

67. ## Math

A military plane maintains an altitude of 15,000 feet over a vast flat desert. It flies at a constant speed on a line that will take it directly over an observer on the ground. At noon, the angle of elevation from the observer’s shoes to the plane is 30

68. ## Math

An airplane is at an altitude of 10 km. You spot the airplane at an angle of 55 degrees . How far away Is the airplane directly from you? Give your answer to the nearest kilometre.

69. ## trigonometry

Two stations A and B are 2,000m apart. When an airplane was directly above A, an observer at B found that the angle of elevation of the airplane is 60° . How far is the plane from the station B??

70. ## physics

If an airplane propeller rotates at 1570 rev/min while the airplane flies at a speed of 333 km/h relative to the ground, what is the linear speed of a point on the tip of the propeller, at radius 1.97 m, as seen by (a) the pilot and (b) an observer on the

71. ## math

an airplane is flying at a constant altitude of 28000 meters. when first seen to the east of the observer, the angle to the airplane is 71.5 degrees. after 73 seconds, the angle of elevation is 51.6 degrees. find the speed of the airplane.

72. ## Math

An airplane flys at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when

73. ## algebra1

A)a plane flies at the height of 1800 feet directly over 150-foot-tall building. how far above the building is the plane? B)the same plane then flies directly over a diver who is 80 feet below the surface of the water. how far is the plane above the diver?

74. ## calculus

An airplane in Australia is flying at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of

75. ## Airplane trig question

An airplane, flying at a speed of 420 miles per hour, flies from point A in the direction 131 degrees for 90 min. and then flies in the direction 41 degrees for 30 min. in what direction does the plane need to fly in order to get back to point A?

76. ## word question in algebra

oh i think i see instead of ft/miles because i changed the 13 miles to ft it would be 0.61 ft/ft An airplane covered 13 miles of its route while decreasing its altitude by 42,000 feet. Find the slope of the airplane's line of descent. Round to the nearest

77. ## Physics

A 15 kg model airplane flies horizontally at point A that is 20 m about point B. It has a speed of 19.993 m/s at point A. It then flies horizontally at point B. If the loss of potential energy is reflected as an increase in kinetic energy, what is the

78. ## Math (Pre-Calc)

An airplane is flying east at a constant altitude of 28,000 meters. When first seen to the east of an observer, the angle of elevation to the airplane is 71.5 degrees. After 73 seconds, the angle of elevation is 51.6 degrees. Find the speed of the

79. ## Geom./Trig.

an airplane flies directly overhead at 540mph. 1 minute later is seen at an angle of elevation of 34 degrees. how far did the airplane fly during that time? what is the elevation of the plane?

80. ## algebra

an airplane is flying at an altitude of 3200 feet. an air- traffic controller in the tower keeps constant track of the planes distance from the tower in X feet. express the horizontal distance from the tower to a point directly below the airplane,d, in

81. ## Physics

A skyrocket explodes 77 m above the ground. Three observers are spaced 106 m apart, with observer A directly under the point of the explosion. Find the ratio of the sound intensity heard by observer A to that heard by observer B. Find the ratio of the

82. ## Physics

An helicopter flies in a strange pattern, all at the same altitude of 5 km: 1) it flies 29 km in a direction 30.0° east of north, 2) it flies 20 km due south, and 3) it flies 10 km in a direction 30.0° north of west. How far did the helicopter end up

83. ## algebra

an airplane flies with a constant speed of 500 miles per hour. How long will it take to travel a distance of 1000 miles?

84. ## algebra

an airplane flies with a constant speed of 500 miles per hour. How long will it take to travel a distance of 1000 miles?

85. ## math

A rocket is fired at an angle of 18.5 ° with the ground from a point 1670 m directly behind an observer. Shortly later the rocket is observed at an angle of elevation of 33.5 ° directly in front of and above the observer. How far on a direct line has the

86. ## Math

A model airplane reaches a maximum altitude and then begin to descend at a constant rate in feet per second. After falling for 12 seconds, the model airplane has an altitude of 212 feet. After falling for 25 second, the model airplane’s altitude is 95

87. ## math

two airplanes left the same airport traveling in opposite direction. if one airplane averages 400 miles per hour and the other airplane averages 250 miles per hour, in how many hours will the distance between the two planes be 1625 miles? Does it help to

88. ## Algebra 1

An airplane flies 750 miles due west in 1 1/2 hours and 750 miles due south in 2 hours. What is the average speed of the airplane?

89. ## science/maps

An airplane flies directly west at 1,000 kilometers per hour. Without changing directions, the plane returns to its starting point in just one hour. What can you infer about the planes route with regard to lines of latitude and longitude? Explain please.

90. ## Math

A plane flies 430 miles at a bearing of N27°E, then turns and flies N63°E for 135 miles. Find the distance and the bearing from the starting point to the ending point ? I found distance to be 450.69 mi by using A^2+B^2=C^2 because it is a right triangle.

91. ## Physics

I have tried this question over and over and not sure if the answer is 16 west or 190 south west please help. Airplane One flies due east at 250 km/h relative to the ground. At the same time, Airplane Two flies 325 km/h, 35° north of east relative to the

92. ## Math

Can some please explain what I have to do to get the answer? An airplane passes directly over Seneca High School. A student at Cherokee High School, which is 4.3 miles away, finds the angle of elevation of the plane to be 19°. Find the altitude of the

93. ## Science

is a an airplane flies with a constant speed of 500 miles per hour how long will it take to travel a distance of 500 miles

94. ## trig

A passenger airplane flying at an altitude of 1.8 km starts its final airport approach by descending at an angle of depression of 6°. How far along the ground is the airplane from its landing point

95. ## Physics

The modern Boeing 747 passenger jet airplane cruises at a speed up to 900 km/hr, at an altitude of 11,000 m. The cabin pressure is maintained equivalent to the atmospheric pressure at an altitude of 2,000 m. This is called the "cabin altitude". The

96. ## Pre Cal

An airplane leaves an airport and flies due west 150 miles and then 230 miles in the direction S 39.67 degrees W. How far is the plane from the airport at this time to the nearest mile.

97. ## math

a vehicle uses 1 tablespoon of gasoline to drive 125 yard how many miles can the vehicle travel per gallon? a model airplane flies 18 feet in 2 seconds what is the planes speed per miles an hour? how do i do these

98. ## physics

An airplane with a speed of 46.4 m/s is climbing upward at an angle of 44° counterclockwise from the positive x axis. When the plane's altitude is 700 m the pilot releases a package. (a) Calculate the distance along the ground, measured from a point

99. ## trig

an airplane leaves the airport and flies due west 150 miles and then 240 miles in the direction 200°40'. Assuming the earth is flat, how far is the plane from the airport at this time( to the nearest mile)?

100. ## Math

An airplane leaves an airport,flies due north for 2 hours at 500 km/h. It then flies on a bearing of 53 degree at 300 km/h for 90 minutes. Find the bearing of the plane from the airport. If it takes the airplane 150 minutes to fly back to the airport,find