84–87
84. What are the magnitude and direction of the vector
85. Given vectors
86. If you walk 12 paces north, 11 paces east, 6 paces south, and 20 paces west, what is the magnitude (in paces) and direction (in degrees relative to the positive x-axis) of the resultant vector formed from the four individual vectors? Round your results to the nearest integer.
87. After a lengthy car ride from a deserted airfield to Seneca Airport, Candace finds herself 250 kilometers north and 100 kilometers west of the airfield. At Seneca, Candace boards a small aircraft that flies an unknown distance in a southwesterly direction and lands at Westsmith Airport. The next day, Candace flies directly from Westsmith to the airfield from which she started her journey. If the flight from Westsmith was 300 kilometers in distance and flew in a direction 15 degrees south of east, how many kilometers was Candace’s flight from Seneca to Westsmith? Round your answer to the nearest integer.
88–96
88. Hans drives 70 degrees north of east at a speed of 50 meters per second. How fast is Hans traveling northward? Round your answer to the nearest integer.
89. If you walk 25 meters in a direction 30 degrees north of west and then 15 meters in a direction 30 degrees north of east, how many meters did you walk in the north-south direction?
90. Jake wants to reach a postal bin at the opposite corner of a rectangular parking lot. It’s located 34 meters away in a direction 70 degrees north of east. Unfortunately, the lot’s concrete was recently resurfaced and is still wet, meaning that Jake has to walk around the lot’s edges to reach the bin. How many meters does he have to walk? Round your answer to the nearest whole meter.
91. If
A: 45 meters at 20 degrees
B: 18 meters at 65 degrees
C: 32 meters at –20 degrees
92. To walk from the corner of Broadway and Park Place to the corner of Church and Barkley in Central City, a person must walk 150 meters west and then 50 meters south. How many meters shorter would a direct route be? Round your answer to the nearest meter.
93. If Jimmy walks 5 meters east and then 5 meters south, what angle does the resultant displacement vector make with the positive x-axis (assuming the positive x-axis points east)?
94. A swimmer can move at a speed of 2 meters per second in still water. If he attempts to swim straight across a 500-meter-wide river with a current of 8 meters per second parallel to the riverbank, how many meters will the swimmer traverse by the time he reaches the other side? Round your answer to the nearest tenth of a kilometer.
95. A basketball rolling at a rate of 10 meters per second encounters a gravel patch that is 5 meters wide. If the basketball is moving in a direction 15 degrees north of east, and if the sides of the gravel patch are aligned parallel to the north-south axis, will the basketball still be rolling by the time it reaches the far side of the patch if the gravel gives it an acceleration of –3 meters per second squared in the same direction it started when it entered the patch? If so, what will be its speed in the easterly direction upon exiting the patch? If not, how many meters (measured perpendicularly to the western edge of the patch) will the basketball roll on the gravel before stopping? Round your numerical response to the nearest integer.
96. Partway through a car trip, a dashboard compass stops working. At the time it broke, Bill had driven 180 kilometers in a direction 70 degrees north of west. He then proceeds to drive 45 kilometers due south on the highway, before turning right and driving 18 kilometers west on Sunset St. When he stops the car, how far is Bill from the location where he began the trip? Round your answer to the nearest kilometer.
97–99
97. A marble rolls off a 2-meter-high, flat tabletop. In how many seconds will it hit the floor? Round your answer to the nearest tenth of a second.
98. Mark rolls a boulder off a cliff located 22 meters above the beach. If he’s able to impart a velocity of 0.65 meters per second to the boulder, how many meters from the base of the cliff will the boulder land? Round your answer to the nearest tenth of a meter.
99. A car flies off a flat embankment with a velocity of 132 kilometers per hour parallel to the ground 45 meters below. With what velocity does the car ultimately crash into the ground? Round your answer to the nearest meters per second.
100–105
100. Alicia kicks a soccer ball with a velocity of 10 meters per second at a 60-degree angle relative to the ground. What is the horizontal component of the velocity? Round your answer to the nearest tenth of a meter per second.
101. The punter for the San Diego Chargers kicks a football with an initial velocity of 18 meters per second at a 75-degree angle to the horizontal. What is the vertical component of the ball’s velocity at the zenith (highest point) of its path? Round your answer to the nearest tenth of a meter per second.
102. A cannonball fired at a 20-degree angle to the horizontal travels with a speed of 25 meters per second. How many meters away does the cannonball land if it falls to the ground at the same height from which it launched? Round your answer to the nearest meter.
103. Launching from a 100-meter-high ski jump of unknown inclination at 40 meters per second, an Olympic athlete grabs 8.2 seconds of hang time before landing on the ground. How far away from the jump does she land?
104. A cannon tilted at an unknown angle fires a projectile 300 meters, landing 11 seconds after launch at a final height equal to its starting one. At what angle was the cannon fired?
105. Will a baseball struck by a bat, giving the ball an initial velocity of 35 meters per second at 40 degrees to the horizontal, result in a home run if it must clear a 1.8-meter-high fence 120 meters away? If it will, by how many centimeters will the ball clear? If not, how many centimeters short will it be? Assume that the ball is struck at a height of 0.8 meters, and round your answer to the nearest 10 centimeters.
Chapter 4
Pushing and Pulling: The Forces around You
Newton’s laws of motion describe how objects move when forces are applied to them. The first law states that an object’s velocity won’t change unless you apply a force to it. One of the most famous and important equations in physics is Newton’s second law: Force equals mass times acceleration. The third law says