1. Less than before. 2. Greater than before. 3. No change. correct
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1 Version One Homework 3 Schemm Oct 22, This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. Vectors are everywhere! Use your knowledge of vectors and math to answer these. Approaching Cars 03:01, highschool, numeric, > 1 min, normal. 001 (part 1 of 3 1 points Two cars approach each other; both cars are moving westward, one at 78 km/h, the other at 64 km/h. What is the magnitude of the velocity of the first car relative to (in the frame of reference of the second car? Correct answer: 14 km/h. All the motion is directed westward, so we can consider west to be positive. The velocity of the first car relative to the second car is v r = v 1 v 2 = 78 km/h 64 km/h = 14 km/h Alternate Let east be positive: The velocity of the first car relative to the second car is v r = v 1 v 2 = 78 km/h ( 64 km/h = 14 km/h which has a magnitude of 14 km/h. 002 (part 2 of 3 1 points What is the direction of the resultant velocity? 1. westward correct 2. eastward 3. Unable to determine. All motion is directed westward, as is their relative velocity. 003 (part 3 of 3 1 points After they pass, how will their relative velocity change? 1. Less than before. 2. Greater than before. 3. No change. correct 4. Unable to determine. There is a change in relative position, but not in relative velocity. Holt SF 03A 01 03:02, highschool, numeric, < 1 min, normal. 004 (part 1 of 2 1 points A truck driver attempting to deliver some furniture travels 8 km east, turns around and travels 3 km west, and then travels 12 km east to his destination. a What distance has the driver traveled? Correct answer: 23 km. d = Let: Let North and East be positive 1 = 8 km, 2 = 3 km, 3 = 12 km, y = 0 km. and d = (8 km + (3 km + (12 km = 23 km. 005 (part 2 of 2 1 points b What is the magnitude of the driver s total displacement? Correct answer: 17 km.
2 Version One Homework 3 Schemm Oct 22, d 1 = Displacement is a vector d 1 = (8 km (3 km + (12 km = 17 km. Holt SF 03A 02 03:02, highschool, numeric, < 1 min, wordingvariable. 006 (part 1 of 2 1 points While following the directions on a treasure map, a pirate walks 45.0 m north, then turns and walks 7.5 m east. a What is the magnitude of the single straight-line displacement that the pirate could have taken to reach the treasure? Correct answer: m. 7.5 m 45 m d = ( 2 + ( y 2 Let north and east be positive: d = 7.5 m y = 45.0 m d = (7.5 m 2 + (45 m 2 = m 007 (part 2 of 2 1 points b At what angle with the north would he have to walk? Correct answer: east of due north. tan = y ( = tan 1 y ( 7.5 m = tan 1 45 m = Holt SF 03B 05 03:02, highschool, numeric, < 1 min, normal. 008 (part 1 of 2 1 points A superhero flies 125 m from the top of a tall building at an angle of 25 below the horizontal. a What is the horizontal component of the superhero s displacement? Correct answer: m. 25 y 125 m = d(cos d = 125 m = 25 = (125 m[cos( 25 ] = m 009 (part 2 of 2 1 points
3 Version One Homework 3 Schemm Oct 22, b What is the vertical component of the superhero s displacement? Correct answer: m. y = d(sin y = (125 m[sin( 25 ] = m Holt SF 03C 01 03:02, highschool, numeric, > 1 min, normal. 010 (part 1 of 2 1 points A football player runs directly down the field for 35 m before turning to the right at an angle of 25 from his original direction and running an additional 15 m before being tackled. a What is the magnitude of the runner s total displacement? Correct answer: m. 35 m 25 d 15 m = d(cos y = d(sin total = y total = y 1 + y 2 d total = ( total 2 + ( y total 2 d 1 = 35 m 1 = 0 d 2 = 15 m 2 = 25 1 = d 1 (cos 1 = (35 m(cos 0 = 35 m y 1 = d 1 (sin 1 = (35 m(sin 0 = 0 m 2 = d 2 (cos 2 = (15 m[cos( 25 ] = m y 2 = d 2 (sin 2 = (15 m[sin( 25 ] = m total = = 35 m m = m y total = y 1 + y 2 = 0 m + ( m = m d total = ( total 2 + ( y total 2 = ( m 2 + ( m 2 = m 011 (part 2 of 2 1 points b At what angle to his original displacement is his total displacement (with counterclockwise positive? Correct answer: x total d total y total
4 Version One Homework 3 Schemm Oct 22, tan total = y total total ( total = tan 1 ytotal ( total m = tan m = to the right of down field. Holt SF 03Rev 50 03:02, highschool, numeric, > 1 min, wordingvariable. 012 (part 1 of 1 1 points A hunter wishes to cross a river that is 1.5 km wide and that flows with a speed of 5.0 km/h. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing if the boat heads directly across the river? Correct answer: min. v re v v br The minimum time occurs when the boat heads directly across the river: = v t = 1.5 km v re = 5.0 km/h v br = 12 km/h We need to find the angle to head into the current so that the resultant direction is perpendicular to the current: Thus and v br sin = v re sin = v re v br = sin 1 ( vre v br ( 5 km/h = sin 1 12 km/h = v = v br cos t min = v = v br cos 1.5 km 60 min = (12 km/h cos h = min Holt SF 03Rev 65 03:02, highschool, numeric, > 1 min, wordingvariable. 013 (part 1 of 2 1 points A car travels due east with a speed of 50.0 km/h. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of 60.0 with the vertical. a Find the magnitude of the velocity of the rain with respect to the car. Correct answer: km/h. The car is moving out from under the rain, so the rain streaks are westward toward the rear bumper. 50 km/h v rc 60.0 v re
5 Version One Homework 3 Schemm Oct 22, Note: Figure is not drawn to scale v rc = v re + v ce sin = v ce v rc For convenience, let down and west be positive: v ce = 50.0 km/h = 60.0 v rc = v ce sin 50 km/h = sin 60 = km/h at 60.0 west of vertical. 014 (part 2 of 2 1 points b Find the magnitude of the rain s velocity with respect to Earth. Correct answer: km/h. straight down. cos = v re v rc v re = v rc (cos = ( km/h(cos 60 = km/h Holt SF 03Rev 66 03:02, highschool, numeric, > 1 min, wordingvariable. 015 (part 1 of 1 1 points A shopper in a department store can walk up a stationary (stalled escalator in 30.0 s. If the normally functioning escalator can carry the standing shopper to the next floor in 20.0 s, how long would it take the shopper to walk up the moving escalator? Assume the same walking effort for the shopper whether the escalator is stalled or moving. Correct answer: 12 s. v pe = v eg = v pg = v pe + v eg l = v pg t t walk = 30.0 s t stand = 20.0 s l t walk l t stand l l v pg = + t walk t stand = l( t stand + t walk ( t stand ( t walk l t = l( t stand + t walk ( t stand ( t walk t = ( t stand ( t walk t stand + t walk (20 s(30 s = 20 s + 30 s = 12 s Holt SF 03Rev 23 03:03, highschool, numeric, > 1 min, wordingvariable. 016 (part 1 of 2 1 points A golfer takes two putts to sink his ball in the hole once he is on the green. The first putt displaces the ball 6.00 m east, and the second putt displaces it 5.40 m south. a How large a displacement would put the ball in the hole in one putt? Correct answer: m.
6 Version One Homework 3 Schemm Oct 22, The displacements are perpendicular, so d = ( 2 + ( y 2 = 6.00 m y = 5.40 m d = (6 m 2 + ( 5.4 m 2 = m 017 (part 2 of 2 1 points b What is the direction (measured from due east, with counterclockwise positive of the displacement? Correct answer: tan = y ( y = tan 1 ( 5.4 m = tan 1 6 m = which is to the south of east. Holt SF 03Rev 29 03:03, highschool, numeric, > 1 min, wordingvariable. 018 (part 1 of 2 1 points A person walks the path shown. The total trip consists of four straight-line paths. 100 m 300 m W N S E a At the end of the walk, what is the magnitude of the person s resultant displacement measured from the starting point? Correct answer: m. 200 m d m 150 m 300 m 150 since 2 = 0 m. since y 1 = 0 m. = d(cos y = d(sin tot = y tot = y 2 + y 3 + y 4 d = ( tot 2 + ( y tot 2 d 1 = m 1 = 0 d 2 = m 2 = 90 d 3 = m 3 = = 150 d 4 = m 4 = = m m 1 = (100 m(cos 0 = 100 m
7 Version One Homework 3 Schemm Oct 22, y 2 = (300 m[cos( 90 ] = 300 m 3 = (150 m[cos( 150 ] = m y 3 = (150 m[sin( 150 ] = 75 m 4 = (200 m(cos 120 = 100 m y 4 = (200 m(sin 120 = m tot = 100 m m 100 m = m and y tot = 300 m 75 m m = m d = ( m 2 + ( m 2 = m 019 (part 2 of 2 1 points b What is the direction (measured from due west, with counterclockwise positive of the person s resultant displacement? Correct answer: tan = y tot tot ( = tan 1 ytot ( tot m = tan m = south of west.
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