A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (3.70 m, 4.10 m) with a velocity of -2.70 m/s and an acceleration of +12.9 m/s². What are the (a) x and (b) y coordinates of the center of the circular path?
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- At 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?In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d₁ = 330 m from the station and at angle 0₁ = 41° above the horizon. The airplane is tracked through an angular change A0 = 118° in the vertical east-west plane; its distance is then d₂ = 850 m. Find the (a) magnitude and (b) direction of the airplane's displacement during this period. Give the direction as an angle relative to due west, with a positive angle being above the horizon and a negative angle being below the horizon. de 731 W Airplane d₁ Radar dishA particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00 m/s i and an acceleration of -12.5 (m/s^2) j . What are the (a) x and (b) y coordinates of the center of the circular path?
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- The figure shows thes initial position i and the final position f of a particle. 4 m i 3 m 3 m 4 m 4m 3 m 5m 3m 2 m 1m What is the initial position vector in unit-vector notation? n 2 m/ Xy 1m! 4m 5m 3 m x .i 3m m î+ i m + i mkb) I(1, 0, 0), J(0, 1, 0), and K(0, 0, 1) 6, A helicopter takes off at a ground velocity of 150 km/h. It climbs at an angle of 48° toward the east. A 17-km/h wind is blowing from the south. Determine the resultant air and ground velocities. Include a diagram in your solution. The Eiffel Tower is 324 m tall. Denise isThe position vector 4.70t|i+ [et + ft2 locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and f are constants. The figure gives the angle e of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° 10 20 -20° t (s) (a) Number Units (b) Number Units
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