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What is a good general rule to follow in order to find the best choice of coordinate system to solve a dynamics problem?

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Vectors

Section: Chapter Questions

Problem 34AP: You are spending the summer as an assistant learning how to navigate on a large ship carrying...

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A roller coaster moves 2.00 102 ft horizontally and then rises 135 ft at an angle of 30.0 above the horizontal. Next, it travels 135 ft at an angle of 40.0 below the horizontal. Use graphical techniques to find the roller coasters displacement from its starting point to the end of this movement.
Figure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.
The layout of the town of Popperville is a perfectly square grid, with blocks 100 feet long (Fig. P3.8). A cat leaves her house and travels to Mike Mulligans place 4 blocks west and 3 blocks north of its starting point. After lapping up the milk that Mike always leaves out, the cat travels an additional 1 block north and 3 blocks east to Mrs. McGillicuttys house. a. On your paper, carefully copy the grid of streets that contains the cats house, Mike Mulligans house, and Mrs. McGillicuttys house. Then draw and label three displacement vectors on your sketch: r1, the cats displacement from her house to Mike Mulligans; r2, the cats displacement from Mike Mulligans to Mrs. McGillicuttys; and rtot, the cats total displacement. b. Write an equation to relate the three displacement vectors you have drawn. c. Is the distance the cat traveled greater than, less than, or equal to the magnitude of the cats total displacement vector? Explain. FIGURE P3.8
Two birds begin next to each other and then fly through the air at the same elevation above level ground at 22.5 m/s. One flies northeast, and the other flies northwest. After flying for 10.5 s, what is the distance between them? Ignore the curvature of the Earth.
At one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?
You fly 32.0 km in a straight line in still air in the direction 35.0 south of west. (a) Find the distances you would have to fly due south and then due west to arrive at the same point. (b) Find the distances you would have to fly first in a direction 45.0south of west and then in a direction 45.0 west of north. Note these are the components of the displacement along a different set of axes-namely, the one rotated by 45 with respect to the axes in (a).
One cubic centimeter of water has a mass of 1.00 103 kg. (a) Determine the mass of 1.00 m3 of water. (b) Biological substances are 98% water. Assume that they have the same density as water to estimate the masses of a cell that has a diameter of 1.00 m, a human kidney, and a fly. Model the kidney as a sphere with a radius of 4.00 cm and the fly as a cylinder 4.00 mm long and 2.00 mm in diameter.
Review. As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 60.0 north of west with a speed of 41.0 km/h. (a) What is the unit-vector expression for the velocity of the hurricane? It maintains this velocity for 3.00 h. at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 25.0 km/h. This new velocity is maintained for 1.50 h. (b) What is the unit-vector expression for the new velocity of the hurricane? (c) What is the unit-vector expression for the displacement of the hurricane during the first 3.00 h? (d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h? (e) How far from Grand Bahama is the eye 4.50 h after it passes over the island?
A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following figure. Use a graphical method (the parallelogram rule) to determine the trapper’s displacement directly to the east and displacement directly to the north that sum up to his resultant displacement vector. If the trapper walked only in directions east and north, zigzagging his way to the lake, how many kilometers would he have to walk to get to the lake?
If , and , find the unknown constants a and b such that .
After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
(a) A car speedometer has a 5% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per how. Note 1 km = 0.6214 mi.