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The parasailing system shown uses a winch to pull the rider in toward the boat, which is traveling with a constant velocity. During the interval when
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Vector Mechanics For Engineers
- The 0.5-lb projectile A is subjected to a drag force of magnitude kv2, where the constant k = 0.0003 lb-sec²/ft2. This drag force always opposes the velocity v. At the instant depicted, v = 210 ft/sec, 0 = 41°, and r = 495 ft. Determine the corresponding values of r and 0. y | ku² Answers: i M. 0 = i 0 T A V 170 --x ft/sec² rad/sec²arrow_forwardAircraft A is flying horizontally at an altitude of 10.6 km and is increasing its speed at the rate of 2 m/s each second. Aircraft B, flying in the same vertical plane at an altitude of 16 km, has a constant speed of 1400 km/h. If A has a speed of 1100 km/h at the instant when 0 = 30°, determine the values of 7 and 0 for this same instant. (* = 12.9 m/s², 0 = −0.0037 rad/s²) A 0 Barrow_forwardAt the instant under consideration, the hydraulic cylinder AB has a length L = 0.75 m, and this length is momentarily increasing at a constant rate of 0.2 m∕s. If vA = 0.6 m∕s and ? = 35°, find the rate of change of the length L in m/s, in order for the velocity of the slider B to be 0.15 m/s.arrow_forward
- A particle moving along the s-axis has a velocity given by v = 22.3 -3.7t² ft/sec, where t is in seconds. When t = 0, the position of the particle is given by so = 3.9 ft. For the first 3.5 seconds of motion, determine the total distance D traveled, the net displacement As, and the value of s at the end of the interval. Answers: Total distance traveled, Net Displacement, The value of s at the end of the interval, D= As = S= i i i ft ft ftarrow_forwardQ15. As shown in the image below, the 17-kg crate is being hoisted by the motor. If at this instant shown the velocity of point P on the cable is vp = 2.6 m/s and the speed is increasing at 1.3 m/s², what is the power input supplied to the motor if its efficiency is e = 0.63? Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper Sl unit. Take g = 9.81 m/s². Vp Your Answer: P Answer D A unitsarrow_forwardA particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 6.3t2 - 7.0t and y = 4.3t2 - t°/4.0. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 3.0 s. Answers: When t = 3.0 s, mm/s, i %3D V = mm/s?, 0x = iarrow_forward
- 2/149 A jet plane flying at a constant speed v at an alti- tude h = 10 km is being tracked by radar located at O directly below the line of flight. If the angle 0 is decreasing at the rate of 0.020 rad/s when e= 60°, determine the value of r at this instant and the magnitude of the velocity v of the plane. Ans. i 4.62 m/s?, v = 960 km/h h Problem 2/149arrow_forwardThe 2-1b spool slides along the smooth horizontal spiral rod, r = (20) ft, where is in radians, as shown in (Figure 1). At the instant = 90°, its angular rate of rotation is constant and equals 0 = 4 rad/s. Figure 8 = 4 rad/s 1 of 1 P Determine the horizontal tangential force P needed to cause the motion. Express your answer in pounds to three significant figures. IVE ΑΣΦ ↓↑ vec P= 6.244 Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining ? lbarrow_forward3. The spatial motion of a particle is described by X = 3t 2 + 4t y = -4t 2 + 3t Z = -6t +9 where the coordinates are measured in feet and the time t is in seconds. (a) Determine the velocity and acceleration vectors of the particle as functions of time. (b) Verify that the particle is undergoing plane motion (the motion is not in a coordinate plane) by showing that the unit vector perpendicular to the plane formed by v and a is constant.arrow_forward
- The rectangular coordinates of a particle which moves with curvilinear motion are given by x = 10.75t +2.25t² - 0.45t³ and y = 6.90 + 17.43t - 2.62t², where x and y are in millimeters and the time t is in seconds, beginning from t = 0. Determine the velocity v and acceleration a of the particle when t = 8 s. Also, determine the first time that the velocity of the particle makes an angle of 30° with the positive x-axis. Answers: V = a = 17.1 10.75 i + i 5.24 i+ i 17.43 j) mm/s j) mm/s²arrow_forwardI Suppose an autonomous surface vessel (ASV) traveling with velocity TvG/O= vi₁ begins to make a turn by adjusting the thrust of its left and right thrusters, TA and TB, respectively. The center of mass of the ASV is located at G and the ASV is symmetric about its vertical axis. The ASV also experiences a drag force that is proportional to its speed and opposes its velocity. At the instant shown, the drag force is D = -kvi₁ where k is a drag coefficient. 1. To model the mass moment of inertia, approximate the ASV as consisting of three rigid bodies: a flat plate as a center body of mass 6m and two slender rods housing the propulsion assemblies, each of mass m, at the outboard sides of the vehicle. Determine the mass moment of inertia, IG, about the vertical axis passing through the center of mass G. (Hint: Use the parallel axis theorem.) 2. At the instant shown, determine the inertial acceleration vector ac/o = axi₁ + ayi2 of the center of mass and the angular acceleration a of the…arrow_forwardA motorboat and its load weigh 2150 N. Assume that the propeller force is constant and equal to 110N, and the water resistance is numerically equal to 6.7V, where V is the speed at any instant time in m/sec. If the boat starts from rest, determine its distance at the end of 10 seconds.arrow_forward
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