Page 43 - Schaum's Outline of Theory and Problems of Applied Physics

28 VECTORS [CHAP. 2

2.8. At what angle west of south should the ship in Question 2.7 have headed to arrive at the same place in a straight path?
(a)22 ◦ (c) 50 ◦
(b)45 ◦ (d)63 ◦

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2.9. A conveyor belt has a velocity of 4.00 m/s at an angle of 40 above the horizontal. The vertical component of its
velocity is
(a) 2.00 m/s (c) 3.06 m/s
(b) 2.57 m/s (d) 3.36 m/s

2.10. An object is acted on by two forces of 20 N each. The angle between the forces is 120 . The resultant force on the
◦
object has the magnitude
(a)20 N (c)34 N
(b)28 N (d)40 N

2.11. A force F has the components F x and F y . The magnitude F x of the force component in the x direction is given by

(a) F − F y (c)
√ F − F y
(b) F − F y
(d) F − F 2
2
y
2.12. Forces of 20 N to the south, 40 N to the northeast, and 10 N to the east act on an object. The magnitude of the resultant
force on the object is
(a)10 N (c)39 N
(b)20 N (d)46 N
2.13. The resultant for the forces in Question 2.12 points
◦
(a)24 east of north (c)52 east of north
◦
◦
◦
(b)45 east of north (d)78 east of north
Supplementary Problems

2.1. Find the length of the hypotenuse of a right triangle whose legs are 483 and 620 m long.

2.2. The hypotenuse of a right triangle is 28 cm long and the length of one of the legs is 23 cm. Find the length of the
other leg.

2.3. Find the values of the unknown sides and angles in the right triangles for which the following data are known (see
Fig. 2-8).

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(a)θ = 45 , a = 10 (d)a = 3, b = 4, c = 5
(b)θ = 15 , b = 4 (e)a = 5, b = 12, c = 13
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(c)θ = 25 , c = 5
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2.4. Two forces, one of 10 N and the other of 6 N, act on a body. The directions of the forces are not known.
(a) What is the minimum magnitude of the resultant of these forces? (b) What is the maximum magnitude?

2.5. A man drives 10 km to the north and then 20 km to the east. What are the magnitude and direction of his displacement
from the starting point?

2.6. Find the magnitude and direction of the resultant force produced by a vertically upward force of 40 N and a
horizontal force of 30 N.

2.7. Find the vertical and horizontal components of a 50-N force that is directed 50 above the horizontal.
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