A young Batman stands 30 ft. away from a hot air balloon that rests on the ground. He has tied a kite string to the bottom of the hot air balloon. As the balloon rises, Batboy notices that he is letting out string at a rate of 10ft./min at the exact time that he has let out 50 ft. of string. How fast is the balloon rising at this time? How fast is the angle between the ground and the string increasing at this time?

Q: A balloon released at point P rises vertically with a constant speed of 6 m/s. Point Q is level with…

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Q: A hot-air balloon rises straight up at a constant speed of 20 feet/sec. An observer stands 200 feet…

A: The speed of the balloon is dydt=20 ft/s2=VyThe distance between observer and launchingpoint, x=200…

Q: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

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Q: A flagpole is 40 feet high and stands on level ground. A flag is attached to a 120 foot rope passing…

A:

Q: A small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

Q: "A Kite 65 feet above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle…

A: Given a kite 65 feet above the ground moves horizontally at a speed of 6 ft/s.

Q: A balloon, leaving the ground 53 ft from an observer, rises 10.75 ft/sec. How fast is the angle of…

A: The given problem is to find the how fast is the angle of elevation of the line of sight increasing…

Q: A child flies a kite at 90ft. The wind is carrying the kite horizontally away from the child at a…

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Q: You are standing 12 feet away from a balloon launcher that will release a balloon vertically up into…

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.