A rocket travels vertically at a speed of 1100 km/hr. The rocket is tracked through a telescope by an observer located 18 km from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 3 min after the lift-off.

Q: An airplane is moving horizontally at 150 mph over an observer at a height of 4,000 ft. How fast is…

A:

Q: A 20-foot-tall tree has fallen against the wall of a garage. The base of the tree starts to slide on…

A:

Q: A ladder 13 ft long leans against a vertical wall. If the top slides down at 3 ft/s, how fast is the…

A: Follow the procedure given below.

Q: A 6 ƒt tall Batman runs (into the night) away from a 10 ft streetlamp at a rate of 1 How fast is his…

A: The diagram of the situation is shown below:

Q: A 10​-ftladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: 1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed…

A: given: A 15-meter ladder is resting against a vertical wall. the bottom of the ladder is being…

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A:

Q: A ladder 15 ft long leans against a vertical wall. If the top slides down at the rate of 2 ft per…

A:

Q: When a rocket is 8 kilometers high, it is moving vertically upward at a speed of 600 kilometers per…

A:

Q: A certain escalator travels at a rate of 13.4 meters per minute, and its angle of inclination is…

A: So from the triangle we have: Answer(a): Vertical component of the velocity is 6.1667 meters per…

Q: A 10 foot ladder is leaning against a wall, with its base 3 feet from the wall. It begins to slide…

A: Given that A 10 foot ladder is leaning against a wall, with its base 3 feet from the wall. It begins…

Q: A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft…

A:

Q: A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude…

A:

Q: A ladder 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: Solved below

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 ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 100 kilometers per…

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: If a ladder of length 20 ft which is leaning against a vertical wall has its upper end sliding down…

A: Given:         Length of ladder =20 ft    dhdt=-2 ft/sec

Q: An airplane is flying horizontally at an altitude of 9000 m. An observer on the ground noticed that…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: It is given that,

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: In a hot-air balloon contest, it was observed that a particular contestant's hot-air balloon rises…

A: The sides and the angles of a triangle are related by the use of trigonometric functions. The…

Q: A bird 150 ft above the ground flies horizontally at a speed of 11 ft/s. At what rate is the angle…

A: Given Data: The height of the bird above the ground is: y=150 ft The speed of the bird is: x'=11…

Q: A plane flying with a constant speed of 9 km/min passes over a ground radar station at an altitude…

A:

Q: When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 600 kilometers per…

A: Set the height of the rocket be h and angle of elevation from the observer's eye is x. dhdt=600

Q: If a ladder of length 20 ft which is leaning against a vertical wall has its upper end sliding down…

A:

Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude…

A:

Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A:

Q: A 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: Given: length of ladder, L=13 ft distance from base, x = 12 ft dxdt=5 ft/sec

Q: When a rocket is 10 kilometers high, it is moving vertically upward at a speed of 1000 kilometers…

A: To determine the rate of change of angle of elevation with respect to observer.

Q: A boy is flying a drone at a constant height of 28 m above the ground. If the drone is moving…

A:

Q: If a ladder of length 20ft which is leaning against a vertical wall has its upper end sliding down…

A: Given : Length of the ladder = 20 ft

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A man walks along a straight path at a speed of 6 ft/s. A searchlight is located on the ground 5 ft…

A: In the question it is asked to calculate at what rate the searchlight is rotating.

Q: A kite 100 ft above the ground moves horizontally at a speed of 4 ft/s. At what rate is the angle…

A: Here we use trigonometric formulas along with differentiation formulas.

Q: A kite 100 ft above the ground moves horizontally at a speed of 3 ft/s. At what rate is the angle…

A: The diagrammatic representation of the problem is shown below.

Q: A ladder 10 ft long leans against a vertical wall. If the bottomof the ladder slides away from the…

A: Given - A ladder 10 ft. long leans against a vertical wall. If the bottom of the ladder slides away…

Q: A man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 30…

A: Given data is : dxdt=4 ft/sec To find the Rate of the searchlight is rotating

Q: A circular blade with a 12-inch diameter spins at a rate of 1800 rpm (revolutions per minute). Find…

A: It is given that a circular blade has diameter 12-inch which spins at the rate of 1800 revolutions…

Q: A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude…

A: given data  constant speed = 24 km/min             altitude = 12 km             angle = 25 degrees…

Q: A kite is flying 25 meters above the flat Earth and being blown by the wind in the horizontal…

A: To calculate rate of change of angle between kite and grounds.  Let theta is the angle between kite…

Q: a television camera is positioned o the ground 4000 feet from the base of a rocket launching pad. If…

A:

Q: A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude…

A:

Q: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude…

A:

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.