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Review. You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a fixed height of 7.60 × 103 m. At time t = 0, the airplane is directly above you so that the vector leading from you to it is
Figure P3.31
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- 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.arrow_forwardYou are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a fixed height of 7.60∗10 3m. At time t=0, the airplane is directly above you so that the vector leading from you to it is P0 =7.60∗10 3j^ m. At t=30.0s, the position vector leading from you to the airplane is P30=(8.04∗10 3i^+7.60∗10 3j^ )m . Determine the magnitude and orientation of the airplanes position vector at t=45.0s.arrow_forwardYou are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 9.00 x 10³ m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P = 9.00 × 10³ m. At t = 30.0 s the position vector leading from you to the airplane is P. = (7.26 × 10³î + 9.00 × 10³ĵ) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 65.0 s. 30 magnitude m direction 26.1 X Your response differs from the correct answer by more than 10%. Double check your calculations.° above the horizontal tei 0 FORMERLY Pa 30arrow_forward
- A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn. The coordinates (meters) of the rabbit's position as functions of time t (seconds) are given by: x = -0.31t2 +7.2t+28 and y = 0,22t² - 9.1t+ 30. A) Att = 15 s, what is the rabbit's position vector in unit-vector notation and n magnitude-angle notation? B) Find the velocity vector at time t = 15 s. c) find the acceleration a at time t = 15s.arrow_forwardYou are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 8.95 103 m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P0 = 8.95 103ĵ m. At t = 30.0 s the position vector leading from you to the airplane is P30 = (7.22 103î + 8.95 103ĵ) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 60.0 s. An illustration shows a woman standing on the ground and facing towards an airplane that is flying away from her. Vector P0 starts at the woman's head and extends vertically to end on a horizontal line that represents the height of the airplane. Vector P30 starts at the woman's head and extends at an angle up and to the right to end on the airplane. What is magnitude ? What is direction in degrees above horizontal?arrow_forwardA golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions: 2. x = (18.0 m/s)t and y = (4.00 m/s)t – (4.90 m/s²) t² (a) Write a vector expression for the ball's position as a function of time, using the unit vectors i and j. By taking derivatives, obtain expressions for (b) the velocity vector v as a function of time and (c) the acceleration vector a as a function of time. Next use unit-vector notation to write ex- pressions for (d) the position, (e) the velocity, and (f) the acceleration of the golf ball, all at t = 3.00 s.arrow_forward
- I start walking. The 1st leg of my trip I walk dA =95m at θA=21° south of east. The 2nd leg of my trip I walk. dB=95m at θB =27° north of east. On my final leg I walk dC =85m at θC=58° north of west. Choose the coordinate system so that x is directed towards the east, and y is directed towards the north. What is magnitude of my displacement vector (in meters) as measured from the origin, and what is the angle of my displacement vector as measured counter clockwise from the x-axis.arrow_forwardA straight river flows east at a speed of 9 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure). The motorboat has a speed of 18 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.) N 60° (a) Express the velocity of the river as a vector in component form. (b) Express the velocity of the motorboat relative to the water as a vector in component form. (Round your answer to two decimal places.) (c) Find the true velocity of the motorboat. (Round your answer to two decimal places.) (d) Find the true speed of the motorboat. (Round your answer to one decimal place.) mi/h Find the direction of the motorboat. (Round your answer to one decimal place.) N ° Earrow_forwardA car goes east at 90 km/h for 0.75 hours, and then turns on a road heading 30° north of east at 88 km/h for 0.5 hour, where the x-axis is east and the y-axis is north. The net displacement (in km) of the car from the starting position, in unit vector notation is: O 105.6i + 22j O 98.1i + 22j O 101.9i + 22j O 86.1i + 22j O 118.5i + 22jarrow_forward
- A straight river flows east at a speed of 8 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure). The motorboat has a speed of 22 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.) 60° (a) Express the velocity of the river as a vector in component form. (b) Express the velocity of the motorboat relative to the water as a vector in component form. (Round your answer to two decimal places.) (c) Find the true velocity of the motorboat. (Round your answer to two decimal places.) (d) Find the true speed of the motorboat. (Round your answer to one decimal place.) mi/h Find the direction of the motorboat. (Round your answer to one decimal place.) ° Earrow_forwardA straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure), The motorboat has a speed of 18 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.) AN 60° (a) Express the velocity of the river as a vector in component form. (b) Express the velocity of the motorboat relative to the water as a vector in component form. (Round your answer to two decimal places.) (c) Find the true velocity of the motorboat. (Round your answer to two decimal places.) (d) Find the true speed of the motorboat. (Round your answer to one decimal place.) mi/h Find the direction of the motorboat. (Round your answer to one decimal place.)arrow_forwardThe route followed by a hiker consists of three displacement vectors → A A → , → B B → , and → C C → . Vector → A A → is along a measured trail and is 2140 m in a direction 21.0° north of east. Vector → B B → is not along a measured trail, but the hiker uses a compass and knows that the direction is 43.0° east of south. Similarly, the direction of vector c is 29.0 ° north of west. the hiker ends up back where she started so the resulting displacment is zero A + B + C =0. Find the magnitude of (a) vector B and (b) Vector c.arrow_forward
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning