52-53 Two cars traveling from the same point but going to different directions Jhun Vert Fri, 05/08/2020 - 10:27 pm

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 Jhun Vert Fri, 05/08/2020 - 10:17 pm

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 Jhun Vert Fri, 05/08/2020 - 10:03 pm

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.
 

40 - Base angle of a growing right triangle Jhun Vert Fri, 05/08/2020 - 09:50 pm

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 Jhun Vert Fri, 05/08/2020 - 09:46 pm

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 Jhun Vert Fri, 05/08/2020 - 09:43 pm

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 Jhun Vert Fri, 05/08/2020 - 09:35 pm

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?
 

37-38 How fast a ship leaving from its starting point Jhun Vert Thu, 05/07/2020 - 08:04 pm

Problem 37
A ship sails east 20 miles and then turns N 30° W. If the ship's speed is 10 mi/hr, find how fast it will be leaving the starting point 6 hr after the start.
 

Problem 38
Solve Problem 37, if the ship turns N 30° E.