Homework #1 Show ALL your work. Credit will not be given on problems in which no work is shown.
1) Estimate the order of magnitude of the length, in meters, of each of the following: (a) a mouse, (b) a pool cue, (c) a basketball court, (d) an elephant, (e) a city block.
2) What types of natural phenomena could serve as time standards?
3) A carpet is to be installed in a room of length 9.72m and width 5.3m. Find the area of the room retaining the proper number of significant figures.
4) How many significant figures are there in (a) 78.9, (b) 3.788 x 109, (c) 2.46 x 10-‐6, (d) 0.0032
5) The speed of light is defined to be 2.99792458 x 108 m/s. Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.
6) A fathom is a unit of length, usually reserved for measuring the depth of water. A fathom is approximately 6 ft in length. Take the distance from Earth to the Moon to be 250 000 miles, and use the given approximation to find the distance in fathoms.
7) A small turtle moves at a speed of 186 furlongs per fortnight. Find the speed of the turtle in centimeters per second. Note that 1 furlong = 220 yards and 1 fortnight = 14 days.
8) A firkin is an old British unit of volume equal to 9 gallons. How many cubic meters are there in 6.00 firkins?
9) A car is traveling at a speed of 38.0 m/s on an interstate highway where the speed limit is 75.0 mi/h. Is the driver exceeding the speed limit? Justify your
10) A ladder 9.00m long leans against the side of a building. If the ladder is inclined at an angle of 75.0o to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?
11) If 𝐵 is added to 𝐴, under what conditions does the resultant vector have a magnitude equal to A + B (the magnitude of both vectors 𝐵 and 𝐴 ? Under what conditions is the resultant vector equal to zero?
12) Vector 𝐴 has a magnitude of 29 units in the positive y-‐direction. When vector 𝐵 is added to vector 𝐴, the resultant vector 𝑅 (𝐴 + 𝐵) points in the negative y-‐ direction with a magnitude of 14 units. Find the magnitude of and direction of 𝐵.
13) Vector 𝐴 has a magnitude of 8.00 units and makes an angle of 45.0O with the positive x-‐axis. Vector 𝐵 also has a magnitude of 8.00 units and is directed along the negative x-‐axis. Find (a) the vector sum 𝐴 + 𝐵 and the vector difference 𝐴 − 𝐵. Draw all the vectors.
14) Vector 𝐴 has a magnitude of 3.00 units and points along the positive x-‐axis. Vector 𝐵 also has a magnitude of 4.00 units and is directed along the negative y-‐axis. Find (a) the vector sum 𝐴 + 𝐵 and the vector difference 𝐴 − 𝐵. Draw all the vectors.
15) A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0O above the horizontal. Next, it travels 135 ft at an angle of 40.0O below the horizontal. Find the coaster’s displacement from its starting point to the end of his movement.
16) A person walks 25.0O north of east for 3.10 km. How far due north and how far due east would she have to travel to arrive at the same location (break the vector into components)?
17) A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?
18) A vector has an x-‐component of -‐25.0 units and a y-‐component of 40.0 units. Find the magnitude and direction (angle) of the vector.