Problem Set 0
A> Measurement (1.1 - 1.3)
1)Convert each of the following into the indicated units.
a)5.00 m to ft
b)1.2 ft/s to m/s
c)60.0 mi/h to km/h
d)9.80 m/s2 to ft/s2
e)90 km/h to m/s
2)A basketball coach insists that his players be at least 180.0 cm tall. Would a player of height 5 ft 11.5 in tall qualify for the team?
3)The depth of the ocean is sometimes measured in fathoms (1 fathom = 6 feet). Distance on the surface of the ocean is sometimes measured in nautical miles (1 nautical mile = 6067 feet). The water beneath a surface rectangle 1.20 nautical miles by 2.60 nautical miles has a depth of 16.0 fathoms. Find the volume of water (in cubic meters) beneath this rectangle.
4)Check the following equations for validity, where x is measured in meters, g and a are in meters/second2, t is in seconds, and v is in meter/second.
a)x 2 = ½ gtb)v2 = 2ax
5)A spring is hanging down form the ceiling and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and is then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation , where k is known as the spring constant. What must be the dimensions k for the equation to be dimensionally correct?
1) (a) 16.4 ft (b) 0.37 m/s (c) 96.6 km/h (d) 32.2 ft/s2 (e) 30 m/s / 2) yes / 3) 3.12 x 108 m34) (a) no (b) yes / 5) k = m/T2 or k measured in kg/s2
B> Trigonometry (1.4)
6)The gondola ski lift at Keystone, Colorado, is 2830 m long. On average, the ski lift rises 14.6 above the horizontal. How high is the top of the ski lift relative to the base?
7)A highway is to be built between two towns, one of which lies 35.0 km south and 72.0 km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west?
8)The silhouette of a Christmas tree is an isosceles triangle. The angle at the top of the triangle is 30.0, and the base measures 2.00 m across. How tall is the tree?
9)A 500.0 m tall building casts a shadow 800.0 m long over level ground. What is the sun’s elevation angle above the horizon?
10)A bridge 50.0 m long crosses a chasm. If the bridge is inclined at an angle of 20.0 to the horizontal, what is the difference in height between the two ends?
11)An observer, whose eyes are 1.83 m above the ground, is standing 32.0 m away from a tree. The ground is level, and the tree is growing perpendicular to it. The observer’s line of sight with the treetop makes an angle of 20.0 above the horizontal. How tall is the tree?
12)The drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride. If edge of the cube is 0.281 nm,what is the distance between the centers of a sodium ion located at one corner of the cube and a chloride ion located on the diagonal at the opposite corner?
6) 713 m / 7) 81.0 km 25.9 / 8) 3.73 m / 9) 32.0 / 10) 17.1 m / 11) 13.5 m / 12) 0.487 nmC> Graphing: Techniques & Evaluation
13) / Age(months) / Weight
(lbs.) / 14) / Volume
(m3) / Pressure
(Pa)
1 / 7.0 / 0.5 / 8.0
2 / 9.4 / 1.0 / 4.0
3 / 10.5 / 2.0 / 2.0
4 / 12.0 / 4.0 / 1.0
5 / 13.0 / 5.0 / 0.8
6 / 14.3 / 8.0 / 0.5
7 / 15.2 / 10.0 / 0.4
8 / 16.7
15) / Time
(s) / Velocity
(m/s) / 16) / Time
(s) / Position
(m)
0.3 / 10 / 0.1 / 0.03
1.2 / 20 / 0.2 / 0.12
2.7 / 30 / 0.5 / 0.75
4.8 / 40 / 1.0 / 3.00
7.5 / 50 / 2.0 / 12.00
10.8 / 60 / 3.0 / 27.00
14.7 / 70 / 4.0 / 48.00
19.2 / 80 / 5.0 / 75.00
DVector Addition (1.5 – 1.6)
17)A displacement vector of magnitude 5.0 m points in an easterly direction. A second displacement vector points north and has a magnitude of 9.7 m. Find the magnitude and direction of the vector sum.
18)A chimpanzee sitting against this favorite tree gets up and walks 51 m due east and 39 m due south to reach a termite mound, where he eats lunch. What is the shortest distance between the tree and the termite mound? What angle does the shortest distance make with respect to due east?
19)The drawing shows a triple jump on a checkerboard, starting at the center of square A and ending on the center of square B. Each side of a square measures 4.0 cm. What is the magnitude of the displacement of the colored checker during the triple jump?
20)A circus performer begins his act by walking out along a nearly horizontal high wire. He slips and falls to the safety net 7.62 m below. The magnitude of his displacement from the beginning of his walk is 8.14 m. How far out along the high wire did he walk? Find the angle that his displacement makes below the horizontal.
17) 10.9 m 62.7 N of E / 18) 64 m 37 / 19) 25 cm / 20) 2.86 m 69EVector Components (1.7)
21)Your friend has slipped and fallen. To help her up, you pull with a force F, as the drawing shows. The vertical component of this force d 130 N while the horizontal component is 150 N. Find the magnitude of F and the angle .
22)An electric field vector, E, has a magnitude of 1.0 N/C and makes an angle of 33 counterclockwise (CCW) from the +x axis. Find the components of E.
23)A magnetic field vector, B, is oriented 65 clockwise from the –y axis. It has a magnitude of 0.010 T. What are the x and y components of this vector?
24)A car drives 2.0 km west, then 8.0 km south, and then 10.0 km at an angle of 53 north of east. Find the car’s final displacement (magnitude and direction).
25)A golfer, putting on a green. Requires three strokes to “hole the ball”. During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20.0 north of east. The third putt is 0.50 m due north. What is the displacement (magnitude and direction relative to due east) would have been needed to “hole the ball” on the very first putt?
26)A football player runs the pattern given in the drawing by three displacement vectors, A, B, and C. The magnitudes of these vectors are A = 5.00m, B = 15.0 m, and C = 18.0 m. Find the resultant vector A + B + C.
27)A baby elephant is stuck in a mud hole. To help pull it out, gamekeepers use a rope to apply a force FA, as part a of the diagram shows. By itself, however, force FA is insufficient. Therefore, two additional forces FB and FC are applied, as in part b of the drawing. Each of these additional forces has the same magnitude F. The magnitude of the resultant force acting on the elephant in part b of the drawing is twice that in part a. Find the ratio F/FA.
28)A sailboat race course consists of four legs, defined by the displacement vectors A, B, C, and D as the drawing indicates. The magnitudes of the first three vectors are A = 3.20 km, B = 5.10 km, and C = 4.80 km. The finish line of the course coincides with the starting line. Find the distance of the fourth leg and the angle .
21) 2.0 x 102 N, 41 / 22) Ex = 0.84 N/C Ey = 0.54 N/C / 23) Bx = -0.0091 T By = -0.0042 T24) 4.0 km east / 25) 7.1 m 9.9 N of E / 26) 30.2 m, 10 / 27) 0.532 / 28) 6.89 km; 26.8