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A spaceship maneuvering near Planet Zeta is located at
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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_forwardLet A⃗ =6î −4ĵ and B⃗ =−3î +7ĵ . What is C⃗ =A⃗ −4B⃗ ? Give your answer as a magnitude and direciton. Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):arrow_forwardQ. At noon, ship A is 200 km east of ship B and ship A is sailing north at 30 km/h. Ten minutes later, ship B starts to sail south at 35 km/h. a. What is the distance between the two ships at 3 pm? b. How fast (in km/h) are the ships moving apart at 3 pm?arrow_forward
- . You are running north at 4.56ms. Another jogger is jogging north at 2.64ms. From your frame of reference, what is the speed and direction of the other jogger? speed of the other jogger in your frame of reference = ms*Round to the nearest hundredth if necessary. Don’t forget that north is in the positive direction and south is in the negative direction.arrow_forwardHow would I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)arrow_forwardA car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 236 m, and the car completes the turn in 35.0 s. 35.0° В (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors î and î m/s? î + m/s? j (b) Determine the car's average speed. m/s (c) Determine its average acceleratiorr during the 35.0-s interval. m/s² î m/s² î +arrow_forward
- The Sun orbits the center of the Milky Way galaxy once each 2.60 × 108 years, with a roughly circular orbit averaging 3.00 × 104 light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit in m/s2.arrow_forwardA car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 263 m, and the car completes the turn 33.0 s. 35.0° (a) What is the acceleration when the car is at B located at an angle of 35.0°7 Express your answer in terms of the unit vectors i and j. m/s? i + |m/s² j (b) Determine the car's average speed. m/s (c) Determine its average acceleration during the 33.0-s interval. m/s? i + m/s? 3arrow_forwardThe figure below shows a particle initially at point A traveling in the +x-direction. It turns in a circular path at constant speed until it is traveling in the +y-direction at point C. The quarter-circle arc from A to C is 207 m in length, and the particle moves from A to C in 35.0 s. Point B on the path is 35.0° below the x-axis. 0 A 35.0⁰ C B x (a) What is the speed of the particle (in m/s)? m/s (b) What is the magnitude and direction of the acceleration when the particle is at point B? (Enter the magnitude in m/s2 and the direction in degrees counterclockwise from the +x-axis.) magnitude m/s² direction ° counterclockwise from the +x-axisarrow_forward
- The Sun orbits the center of the Milky Way galaxy once each 2.60 × 108 years, with a roughly circular orbit averaging 3.00 × 104 light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the average speed of the Sun in its galactic orbit in m/s.arrow_forwardA student standing on a cliff throws a stone from a vertical height d=8.0m above the level ground with velocity v0=16.2m/s at an angle θ=34∘ below the horizontal. It moves without air resistance. Use a Cartesian coordinate system with the origin at the stone's initial position. 1).With what speed, in meters per second, does the stone strike the ground? 2) which option is correct If the stone had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal, then compare their impact velocities. The impact velocity when throwing a stone above horizontal will be more than the case when throwing a stone below horizontal. The impact velocities of the two situations will be the same. More information is needed to conclude the relative strength of impact velocities. The impact velocity when throwing a stone above horizontal will be less than the case when throwing a stone below horizontal.arrow_forwardThe figure below shows a particle initially at point A traveling in the +x-direction. It turns in a circular path at constant speed until it is traveling in the +y-direction at point C. The quarter-circle arc from A to C is 252 m in length, and the particle moves from A to C in 41.0 s. Point B on the path is 35.0° below the x-axis. What is the speed of the particle (in m/s)? What is the magnitude and direction of the acceleration when the particle is at point B? (Enter the magnitude in m/s2 and the direction in degrees counterclockwise from the +x-axis.)arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning