A boat is sailing at a rate of 10 feet per second away from an observer 5 feet above the boat. How fast is the angle from the observer to the boat changing when the boat is a horizontal distance of 30 feet away from the observer?

Q: You are facing a building that is 150 feet higher than your transit, and you must elevate your…

A:

Q: High-speed stroboscopic photographs show that the head of a 200-g golf club is traveling at 40 m/s…

A: Given,      mclub…

Q: A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the…

A: Given: The angle of elevation of the balloon is 65°, and the rate of pulling of rope is 5 ft /s.…

Q: raveling due north at 570 mi/hr. Assuming both airliners maintain their (equal) elevations, how fast…

A: In this question, the concept of the derivative is applied to calculate the rate of change.…

Q: eading due north at 500 km/h. If it encounters a wind from the northeast at 1 sultant velocity…

A: We will solve the problem.

Q: Find the Linear Speed of an Object Traveling in Circular Motion

A: The linear speed of a point on a rotating object depends on its distance from the center of…

Q: At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 24 knots and ship…

A: At time t, the ship A moves 24t and ship B moves 16t. It can be found that, the ship A moves closer…

Q: Mo is on a baseball team and hears that a ball thrown at a 44 degree angle from the ground will…

A: Given, Mo is on a baseball team and hears that a ball thrown at a 44 degree angle from the ground…

Q: A balloon was rising vertically in the air from the ground level that was 12 feet away from an…

A: Given,  a balloon was rising vertically in the air from the ground level that was 12 feet away from…

Q: A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10…

A:

Q: A street light is at the top of a 18 foot tall pole. A 6 foot tall woman walks away from the pole…

A: Let AB be the pole=18ft CD be height of woman=6 ft let AD=x and DE=y dxdt=4 ft/sec (given)

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.