. . so/ve prob/ems 510 algebraically . . Y some of them graphical/y to check $323335}: solve displacement? 6. You first walk 8.0 km north from ho . . me th east until your displacement from home i? walk 10.0 km. How far east did you walk? 7. In a coordinate system in which the positive xaxrs IS east, for what range of angles is the xcomponent positive? For what range is it negave? 8. Could a vector ever be shorter than one of its components? Could a vector ever be equal in length to one of its components? Explain. 9. Two ropes tied to a tree branch hold up a child's swing as shown in Figure 7. The tension in each rope is 2.28 N. What is the combined force (magnitude and direction) of the two ropes on the swing? 10. CHALLENGE Afua and Chrissy are going to sleep overnight in their tree house and are using some ropes to pull up a 3.20-kg box containing their pillows and blankets. The girls stand on different branches, as shown in Figure 8, and pull at the angles with the forces indicated. Find the x and Y-COmponents of the initial net force on the box. Hint: Draw a free-body diagram so you do not leave out a force. .. , mumaammmmw 10 on incline play horizontal angle and vertical are the some , ) aslet of mass sky is pulled over snow by a yoon force on a rope that makes an angle with the ground of 83.19, if ff = loop How long will it take the sled to reach loings 3. LIGONVVIIUII Lllv w-g of the resultant vector. 32 = A2 + 52 2AB(COS 92) _ 56 R: A2+82 2AB(co 2) '5ubgfufeAszskm'3='s' = (25 km)? + (15 km)2 4 2(25 km)(15 km)(005 135) :37 km E EVALUATE THE ANSWER - Are the units correct? Each answ 0 Do the signs make sense? The sums are posntive. - Are the magnitudes realistic? From the sketch, you C longer than either vector. er is a length measured in kilometers. an see the resultant should be 1. A car is driven 125.0 km due west then 65.0 km due south. What is the magni- tude of its displacement? Solve this problem both graphically and mathematl- cally, and check your answers against each other. 2. Two shoppers walk from the door of the mall to their car.~They walk 250.0 m down a lane of cars, and then turn 90 to the right and walk an additional 60.0 m. How far is the shoppers' car from the mall door? Solve this problem both graphi- cally and mathematically, and check your answers against each other. 3. A hiker walks 4.5 km in one direction then makes a 45 turn to the right and walks another 6.4 km. What is the magnitude of the hiker's displacement? \\ '\\ 4. CHALLENGE An ant crawls on the sidewalk. It first moves south a distance of 5.0 cm. It then turns southwest and crawls 4.0 cm W ' - ant's displacement? ' hat IS the magnltude 0f the 124 Chapter 5 . Displacement and Force in Two Dimensions