62. A ferry boat is traveling east at 1.3 meters per second when the captain notices a boat in its path. The captain engages the reverse motors so that the ferry accelerates to the west at 0.2 meters per second per second. After 20 seconds of this acceleration, what is the boat’s position with respect to its initial position?
63–66
63. A cheetah can accelerate from 0 miles per hour to 60 miles per hour in 20 meters. What is the magnitude of its acceleration?
64. A speedboat can accelerate from an initial velocity of 3.0 meters per second to a final velocity that is 3 times greater over a distance of 42 meters. What is the magnitude of its acceleration?
65. You drop a feather from your balcony, which is 4.5 meters above the ground. After falling 0.20 meters, it moves at the speed of 0.30 meters per second. What is the magnitude of its acceleration?
66. A boat moving north at 2.3 meters per second undergoes constant acceleration until its speed is 1.2 meters per second northward. With respect to its initial position, its final position is 200 meters northward. What is its acceleration?
67–70
67. A boat accelerates at 0.34 meters per second per second northward over a distance of 100 meters. If its initial velocity is 2.0 meters per second northward, what is its final velocity?
68. A train brakes to a stop over a distance of 3,000 meters. If its acceleration is 0.1 meter per second per second, what is its initial speed?
69. To pass another race car, a driver doubles his speed by accelerating at 4.5 meters per second per second for 50 meters. What are his initial and final speeds?
70. From a position 120 meters above a pigeon, a falcon dives at 9.1 meters per second per second, starting from rest. After diving 25 meters, the falcon stops accelerating. What is the falcon’s speed when it strikes the pigeon?
Chapter 3
Moving in a Two-Dimensional World
The basic quantities you use to describe motion in two dimensions – displacement, velocity, and acceleration – are vectors. A vector is an object that has both a magnitude and a direction. When you have an equation that relates two vectors, you can break each vector into parts, called components. You end up with two equations, which are usually much easier to solve.
The Problems You’ll Work On
In this chapter on two-dimensional vectors and two-dimensional motion, you work with the following situations:
✓ Adding and subtracting vectors
✓ Multiplying a vector by a scalar
✓ Taking apart a vector to find its components
✓ Determining the magnitude and direction of a vector from its components
✓ Finding displacement, velocity, and acceleration in two dimensions
✓ Calculating the range and time of flight of projectiles
What to Watch Out For
While you zig and zag your way through the problems in this chapter, avoid running into obstacles by:
✓ Identifying the correct quadrant when finding the direction of a vector
✓ Finding the components before trying to add or subtract two vectors
✓ Breaking the displacement, velocity, and acceleration vectors into components to turn one difficult problem into two simple problems
✓ Remembering that the vertical component of velocity is zero at the apex
✓ Recognizing that the horizontal component of acceleration is zero for freely falling objects
71–72
71. How many numbers are required to specify a two-dimensional vector?
72. Marcus drives 45 kilometers at a bearing of 11 degrees north of west. Which of the underlined words or phrases represents the magnitude of a vector?
73–75
73. Vector U points west, and vector V points north. In which direction does the resultant vector point?
74. If vectors A, B, and C all point to the right, and their lengths are 3 centimeters, 5 centimeters, and 2 centimeters, how many centimeters long is the resultant vector formed by adding the three vectors together?
75. Initially facing a flagpole, Jake turns to his left and walks 12 meters forward. He then turns completely around and walks 14 meters in the opposite direction. How many meters farther away from the flagpole would Jake have ended had he started his journey by turning to the right and walking 14 meters and then turning completely around and walking the final 12 meters?
76–79
76. If
77. If
78. Given that
79. Given the three vectors
80–83
80. Vector A has a magnitude of 28 centimeters and points at an angle 80 degrees relative to the x-axis. What is the value of
81. Vector C has a length of 8 meters and points 40 degrees below the x-axis. What is the vertical component of C, rounded to the nearest tenth of a meter?
82. Jeffrey drags a box 15 meters across the floor by pulling it with a rope. He exerts a force of 150 newtons at an angle of 35 degrees above the horizontal. If work is the product of the distance traveled times the component of the force in the direction of motion, how much work does Jeffrey do on the box? Round to the nearest ten newton-meters.
83. Three forces pull on a chair with magnitudes of 100, 60, and 140, at angles of 20