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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_forwardFind (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.)arrow_forwardOne student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?arrow_forward
- 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.arrow_forwardTwo points in the xy plane have Cartesian coordinates (2.00, 4.00) m and (3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates.arrow_forward1.54 · An acre, a unit of land measurement still in wide use, has a length of one furlong ( mi) and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat land to a depth of 1 foot. How many gallons are in 1 acre-foot?arrow_forward
- The polar coordinates of a certain point are (r = 3.15 cm, 0 = 262°). (a) Find its Cartesian coordinates x and y. x = |-0.438 cm = |-0.312 Your response is off by a multiple of ten. cm (b) Find the polar coordinates of the points with Cartesian coordinates (-x, y). = |1.41 Your response differs from the correct answer by more than 10%. Double check your calculations. cm = |-45 Your response differs from the correct answer by more than 10%. Double check your calculations. (c) Find the polar coordinates of the points with Cartesian coordinates (-2x, -2y). = 2.83 Your response differs from the correct answer by more than 10%. Double check your calculations. cm 225 The response you submitted has the wrong sign. %3D (d) Find the polar coordinates of the points with Cartesian coordinates (3x, -3y). = 4,24 Your response differs from the correct answer by more than 10%. Double check your calculations. cm 9 = -45 Need Help? Read Itarrow_forwardProblem 4: Two points in a plane have polar coordinates P1(2.4 m, Jt/6) and P2(3.8 m, 2jt/3). P1(, y) m 20% Part (a) Determine the x value of the Cartesian coordinates for Pj.arrow_forwardProblem 2: A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west corner, she measures the first side to be 72 m long and the next to be 112 m. These sides are represented as displacement vectors A and B in the figure. She then correctly calculates the length of the third side C. What is her result (in meters)? ICI = || y C = ? m A A+B+C =0 0= ? A 21° B B 11° x W N S Earrow_forward
- ds and a = dt dv Suppose quantity s is a length and quantity t is a time. Suppose the quantities v and a are defined by v = dt (Use the following as necessary: L and T.) (a) What is the dimension of v? [v] = (b) What is the dimension of the quantity a? [a] = (c) What is the dimension of v dt? (d) What is the dimension of a dt? dt| = da (e) What is the dimension of dt da dtarrow_forwardWhich of the following is not true? ○ V1 (1) V2 (2) = V₁ (2) √₂ (1) ○ V1 (1) V2 (2) + $1 (2) 42 (1) = V1 (2) √2 (1) + V1 (1) ½₂ (2) O All equations are true. O All equations are incorrect. ○ V1 (1) V₂ (2) — V₁ (2) V₂ (1) − −V1 (2) V₂ (1) + V1 (1) √2 (2) =arrow_forwardA particle of mass m is projected vertically upwards with velocity vo from the surface of the Earth at z = 0. Gravity acts downwards in the negative z direction, with expression F₁ = GmM (a+z)² where a is the radius of the Earth, M its mass, and G is the gravitational constant. Suppose that the particle is also subject to a constant friction force F₂ = -mfk, with ƒ>0. (a) What are the dimensions of f? (b) Write the equation of motion and use it to show that the equation for the velocity v(z) is given by v² = v₁ + 2GM a+z where vo> 0 is the initial velocity at z = 0. (c) Show that there is no escape velocity and find the maximum height reached by the particle. Answers should be given in terms of a, M, vo, G and f. 2GM a -2fz,arrow_forward
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