Page 42 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 2] VECTORS 27

Now we add the values of the x components to get R x and add the values of the y components to get R y :
R x = A x + B x + C x = 0 − 2.0 km/h + 4.3 km/h = 2.3 km/h
R y = A y + B y + C y = 8.0 km/h + 0 − 2.5 km/h = 5.5 km/h

The magnitude of the resultant R is therefore

√

2 2 2 2
R = R + R = (2.3 km/h) + (5.5 km/h) = 35.54 km/h = 6.0 km/h
x
y
The boat’s velocity relative to the earth’s surface is 6.0 km/h.
The direction in which the boat is moving relative to the earth’s surface can be given in terms of the angle θ
between R and the +y axis, which is north. Since
R x 2.3 km/h
tan θ = = = 0.418 θ = 23 ◦
R y 5.5 km/h
the boat’s direction of motion is actually 23 to the east of north even though it is headed north [Fig. 2-17(d)].
◦

Multiple-Choice Questions

2.1. A box suspended by a rope is pulled to one side by a horizontal force. The tension in the rope
(a) is less than before
(b) is unchanged
(c) is greater than before
(d) may be any of the above, depending on how strong the force is

2.2. The minimum number of unequal forces whose vector sum can equal zero is
(a)2 (c)4
(b)3 (d)6
2.3. When two vectors are added together, their resultant is a minimum when the angle between them is
(a)0 (c)90 ◦
(b)45 ◦ (d) 180 ◦

2.4. Of the following pairs of forces, which one or more cannot be added to give a resultant force of 2 N?
(a) 1Nand1N (c) 1Nand3N
(b) 1Nand2N (d) 1Nand4N

2.5. Of the following sets of displacements, which one or more might be able to return a car to its starting point?
(a) 3, 4, 12, and 20 km (c) 20, 60, 80, and 180 km
(b) 5, 10, 15, and 20 km (d) 100, 100, 100, and 100 km

2.6. A boat whose velocity through the water is 14 km/h is moving in a river whose current is 6 km/h relative to the
riverbed. The velocity of the boat relative to the riverbed must be between

(a) 6 and 14 km/h (c) 8 and 14 km/h
(b) 6 and 20 km/h (d) 8 and 20 km/h

2.7. A ship travels 200 km to the south and then 400 km to the west. The ship’s displacement from its starting point is
(a) 200 km (c) 450 km
(b) 400 km (d) 600 km