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In Chapter 3, you’ll learn that the range of a projectile launched over level ground is given by
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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 1.69arrow_forwardFigure OQ1.13 shows two vectors D1 and D2. Which of the possibilities (a) through (d) is the vector D22D1, or (e) is it none of them? Figure OQ1.13arrow_forwardThree displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44arrow_forward
- Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and 6.60 cm, respectively. If AB+3C=0, what are the components of C?arrow_forwardWhat is the y component of the vector shown in Figure OQ1.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e) none of those answers Figure OQ1.9 Objective Questions 9 and 10.arrow_forwardWhat is the x component of the vector shown in Figure OQ1.9? (a) 3 cm (b) 6 cm (c) 4cm (d) 6cm (e) none of those answers Figure OQ1.9 Objective Questions 9 and 10.arrow_forward
- A delivery man starts at the post office, chives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Use a graphical method to find his net displacement vector.arrow_forwardA person going for a walk follows the path shown in Figure P1.51. The total trip consists of four straight-line paths. At the end of the walk, what is the persons resultant displacement measured from the starting point? Figure P1.51arrow_forwardCalculate the result for each of the following cases using the correct number of significant figures. a. 3.07670 10.988 b. 1.0093 105 9.98 104 c. 5.44231064.008103arrow_forward
- An engineer designs a roller coaster so that a car travels horizontally for 172 ft, then climbs 147 ft at an angle of 32.0° above the horizontal. It then moves 147 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.) Sig figs Considered.arrow_forwardGiven the vector techniques you worked on in the lab, answer the follow question: suppose you first walk 12 m in a direction 20° west of north, then 20 m in a direction 40° south of west, then 14 m in a direction 30° east of north, and finally 19 m in a direction 40° east of south. How far are you (as the crow flies) from your starting point, and what is the compass direction (west of south) of a line connecting your starting point to your final position?arrow_forwardAn engineer designs a roller coaster so that a car travels horizontally for 202 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. It then moves 137 ft at an angle of 40.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.) magnitude ft direction Need Help? Read It counterclockwise from the +x-axisarrow_forward
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