MATHalinoEngineering MathematicsProblem 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.
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.
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.
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.
Problem 43
A ship lies 6 miles from shore, and opposite a point 10 miles farther along the shore another ship lies 18 miles offshore. A boat from the first ship is to land a passenger and then proceed to the other ship. What is the least distance the boat can travel?
Problem 44
Two posts, one 8 feet high and the other 12 feet high, stand 15 ft apart. They are to be supported by wires attached to a single stake at ground level. The wires running to the tops of the posts. Where should the stake be placed, to use the least amount of wire?
Problem 45
A ray of light travels, as in Fig. 39, from A to B via the point P on the mirror CD. Prove that the length (AP + PB) will be a minimum if and only if α = β.
Problem 1011
A ship being launched slides down the ways with constant acceleration. She takes 8 sec to slide (the first foot | 0.3048 meter). How long will she take to slide down the ways if their length is (625 ft | 190.5 m)?