## 55 - Greatest angle subtended by a picture

Problem 55
The lower edge of the picture is a ft, the upper edge is b ft, above the eye of an observer. At what horizontal distance should he stand, if the vertical angle subtended by the picture is to be greatest?

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

Problem 52
A car drives south at 20 mi/hr. Another car, starting from the same point at the same time and traveling 40 mi/hr, goes east for 30 minutes then turns north. Find the rate of rotation of the line joining the cars (a) 1 hour after the start; (b) at the time the second car makes its turn.

Problem 53
Prove that the results in Problem 52 are independent of the speed of the cars, if the second car travels twice as fast as the first car.

## 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.

Problem 51
Show that the answers to Problem 49 are independent of the speed of the ship.

## 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.

Problem 47
In Problem 46, find when the light rotates most rapidly.

Problem 48
Prove that the result in Problem 46 and Problem 47 are independent of the speed of the ship.

## 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?