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- A hiker walks from (x1, y1) = (4.00 km. 3.00 km) to (x2, y2) = (3.00 km, 6.00 km), (a) What distance has the traveled? (b) The hiker desires to return to his starting point. In what direction should he go? (Give the angle with respect to due cast.) (See Sections 3.2 and 3.3.)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 1.69What is the y component of the vector (3i 8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answers
- A ball is released from rest at the top of an incline whose height 16.1 centimeters and base 116.6 centimeters. Taking x0 = 0 at the top of the incline, the horizontal location(along the base, in centimeters) of the ball after 1.02 seconds is:A ball is released from rest at the top of an incline whose height 8.5 centimeters and base 54.9 centimeters. Taking xo = 0 at the top of the %3D incline, the horizontal location (along the base, in centimeters) of the ball after 0.52 seconds is:At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 9.00 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 40.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?
- At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 9.00 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 40.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? Answer: 34.4 yards What if? The receiver that catches the football travels 67.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run? _______________________yardsAn engineer designs a roller coaster so that a car travels horizontally for 192 ft, then climbs 147 ft at an angle of 33.00 above the horizontal. It then moves 147 ft at an angle of 42.0° 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 The magnitude of the displacement is the length of the vector which goes from the starting point to the ending point. You will need to measure this distance, and multiply by your scale factor. ft direction ° counterclockwise from the +x-axisAt a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 9.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 60.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? What if? The receiver that catches the football travels 60.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?
- At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 8.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 55.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? yards (b) What if? The receiver that catches the football travels 64.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 7.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 50.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?What if? The receiver that catches the football travels 65.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?A ball is released from rest at the top of an incline whose height 19.1 centimeters and base 59.3 centimeters. Taking x0 = 0 at the top of the incline, the horizontal location (along the base, in centimeters) of the ball after 0.552 seconds is: