# time rates

## 52-53 Two cars traveling from the same point but going to different directions

## 49-51 Ship sailing east and turned N 30d E

**Problem 49**

A ship, moving 10 mi/hr, sails east for 2 hours, then turns N 30° E. A searchlight, placed at the starting point, follows the ship. Find how fast the light is rotating (a) 4 hours after the start; (b) just after the turn.

## 46-48 Rate of rotation of the searchlight

**Problem 46**

A ship, moving at 8 mi/hr, sails east for 2 hr, then turns N 30° W. A searchlight, placed at the starting point, follows the ship. Find how fast the light is rotating, (a) 3 hr after the start; (b) just after the turn.

## 45 - Angle of elevation of the the kite's cord

**Problem 45**

A kite is 60 ft high with 100 ft of cord out. If the kite is moving horizontally 4 mi/hr directly away from the boy flying it, find the rate of change of the angle of elevation of the cord.

## 44 - Angle of elevation of the rope tied to a rowboat on shore

**Problem 44**

A rowboat is pushed off from a beach at 8 ft/sec. A man on shore holds a rope, tied to the boat, at a height of 4 ft. Find how fast the angle of elevation of the rope is decreasing, after 1 sec.

## 40 - Base angle of a growing right triangle

**Problem 40**

The base of a right triangle grows 2 ft/sec, the altitude grows 4 ft/sec. If the base and altitude are originally 10 ft and 6 ft, respectively, find the time rate of change of the base angle, when the angle is 45°.

## 39 - Rate of increase of angle of elevation of the line of sight

**Problem 39**

A balloon, leaving the ground 60 ft from an observer, rises 10 ft/sec. How fast is the angle of elevation of the line of sight increasing, after 8 seconds?

## 38 - Rate of rotation of search light pointing to a ship

**Problem 38**

A ship, moving 8 mi/hr, sails north for 30 min, then turns east. If a searchlight at the point of departure follows the ship, how fast is the light rotating 2 hr after the start.

## 37 - A ladder sliding downward

**Problem 37**

A ladder 15 ft long leans against a vertical wall. If the top slides down at 2 ft/sec, how fast is the angle of elevation of the ladder decreasing, when the lower end is 12 ft from the wall?

## Problems in Caculus Involving Inverse Trigonometric Functions

The following are problems involving inverse trigonometric functions.