A car in a roller coaster moves along a track that consists of a sequence of ups anddowns. Let the x axis be parallel to the ground and the positive y axis point upward.In the time interval from t 0 tot = = 4s, the trajectory of the car along acertain section of the track is given by7 = A(1 m/s)ti + A [(1 m/s³) t³ - 6(1 m/s²)t²]ĵwhere A is a positive dimensionless constant. At tcar ascending or descending?=2.0 S is the roller coasterAscending.Descending.

Step 1: Step 2: Step 3: Step 4:

Answered: A car in a roller coaster moves along a…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section6.3: Relative Velocity

Problem 27PP

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A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69
In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day and he is blown along the following directions: 2.50 km and 45.0 north of west, then 4.70 km and 60.0 south of east, then 1.30 km and 25.0 south of west, then 5.10 km straight east, then 1.70 km and 5.00 east of north, then 7.20 km and 55.0 south of west, and finally 2.80 km and 10.0 north of east. Use a graphical method to find the castaway’s final position relative to the island.
A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed vi. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?
A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.70 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 2.35 m high, and from there it will fall into a pool (Fig. P3.42). (a) Will the space behind the waterfall be wide enough for a pedestrian walkway? (b) To sell her plan to the city council, the architect wants to build a model to standard scale, which is one-twelfth actual size. How fast should the water flow in the channel in the model? Figure P3.42
Find (a) the x- and (b) y-components of R = 2A B if A has components Ax = 15.0 m and Ay = 12.0 m whereas B has components Bx = 24.0 m and By = 8.00 m. (See Section 3.2.)
In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day, and she is blown along the following straight lines: 2.50 km and 45.0 north of west, then 4.70 km and 60.0 south of east, then 130 km and 25.0 of west, then 5.10 km due east, then 1.70 km and 5.00 east of north, then 7.20 km and 55.0 south of west, and finally 2.80 km and 10.0 north of east. Use the analytical method to find the resultant vector of all her displacement vectors. What is its magnitude and direction?
Figure OQ3.3 shows a birds-eye view of a car going around a highway curve. As the car moves from point 1 to point 2, its speed doubles. Which of the vectors (a) through (e) shows the direction of the cars average acceleration between these two points?
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.
If , and , find the unknown constants a and b such that .
Vector B has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of B and (b) the angle that B makes with each coordinate axis.
In the blizzard of ’88, a rancher was forced to drop hay bales from an airplane to feed her cattle. The plane flew horizontally at 160 km/hr and dropped the bales from a height of 80 m above the flat range, (a) She wanted the bales of hay to land 30 m behind the cattle so as to not hit them. Where should she push the bales out of the airplane? (b) To not hit the cattle, what is the largest time error she could make while pushing the bales out of the airplane? Ignore air resistance.
The same vectors that are shown in Figure P3.6 are shown in Figure P3.42. The magnitudes are F1 = 1.90f, F2 = f, and F3 = 1.4f, where f is a constant. a. Use the coordinate system shown in Figure P3.42 to find R=F1+F2+F3 in component form in terms of f. b. If Rx = 0.33, what is Ry? c. Check your result by comparing your answer to that of Problem 6. FIGURE P3.42

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