Plane trigonometry with practical applications, by Leonard E. Dickson.

Ch. III]

TRAVERSE TABLE

31

EXERCISES ON RESULTANTS AND COMPONENTS OF FORCES
1. Two forces of 5 and 12 pounds act at right angles to each other.
Find the resultant force (without using tables) and the angle which it
makes with the second force.
2. A sled is pulled along a level road by a force of 65 pounds, the direction of the pull making 50~ with the horizontal. Find the forward pull on
the sled.
3. Two men lift a weight by means of ropes in the same vertical plane.
One man pulls 42 pounds in a direction making 22~ with the vertical and
the other 63 pounds in a direction making 43~ with the vertical. How
heavy is the weight?
4. A ship, always headed due east, steams at a speed which would
carry it 12 miles per hour in still water. But, on account of a current
running due south, its actual speed is 13.5 miles per hour and its track
in the water makes an angle of 27~ with an easterly direction. Find the
velocity of the current.
5.* Each half of a bridge is inclined 8~ to the horizontal. Find the
vertical pressure and the horizontal thrust (i.e., pressure) upon the two
supporting piers at the ends when the bridge bears 40 tons at its middle.
6. A horse pulls with a force of 400 pounds along a towline making
7~ with the direction of a canal. Find the effective force on the boat.
7. Find without tables the magnitude of the resultant of a force of
30 pounds acting southwest with a force of 40 pounds acting southeast.
8.* Resolve a force of 100 pounds into two equal components whose
directions make an angle of 70~ with each other.
22. Refraction of light. When a ray of light AB passes from
the air into water, it does not
continue in its former direc-
tion ABE, but is said to be
refracted into a new direc-
tion BC (Fig. 21). The angle G
i which the incident ray AB \
makes with the perpendicular PB to the surface of the Q C r
water is called the angle of -SD
incidence. The angle r which FIG. 21