#1. A particle undergoes acceleration å while moving from 1 point 1 to point 2. Which of the choices shows the most likely velocity vector v, as the particle leaves point 2? 2.
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- At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 nor 90 : (a) Is the acceleration ever zero? (b) Is the vector v ever parallel or antiparallel to the vector a? (c) Is the vector v ever perpendicular to the vector a? If so, where is this located?A particle is traveling in a circular path at constant speed in four positions as shown below. If theta1 = 74.00, theta2 = 1550, theta3 = 1950, and theta4 = 2920, determine the angles, relative to the positive-x axis, at which the particle is accelerating.
- At t=0, a particle is projected with a speed Vo at angle theta from a cliff point H=100m from ground level as shown. It is seen at time t=2s, having a velocity v(t2)=8i ‐ 11j m/s according to the coordinate system shown. You must use this coordinate system and origin O. a)Find V o, and theta o. b) If the cliff height is H=100m, write a numerical expression for (t2) in unit vector notation. You must use the origin O and then draw r (t2) on the diagram. c)Find R, the horizontal distance the object has traveled when it reaches its highest point.Suppose you take two steps and (that is, two nonzero displacements). Under what circumstances can you end up at your starting point? More generally, under what circumstances can two nonzero vectors add to give zero? Is the maximum distance you can end up from the starting point A+B the sum of the lengths of the two steps?From the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim//s and moves in the xy plane with a constant acceleration of veca=(-9.0hati+3.0hatj)m//s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?
- A seasoned mini golfer is trying to make par on a tricky number five hole. The golfer can complete the hole by hitting the ball from the flat section it lays on, up a 45∘45∘ ramp, over a moat, and into the hole which is ?=1.90 md=1.90 m away from the end of the ramp. If the opening of the hole and the end of the ramp are at the same height, ?=0.880 m,y=0.880 m, at what speed must the golfer hit the ball to launch the ball over the moat so that it lands directly in the hole? Assume a frictionless surface, so the ball slides without rotating. The acceleration due to gravity is 9.81 m/s2.Anwser ALL You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (−134 m, 26 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and −70.0), then (−20.0 and cy), then (−61.0 and −68.0). (a) What is component bx? (b) What is component cy? (c) What is the the magnitude of the overall displacement? (d) What is the angle of the overall displacement? ? counterclockwise from the +x-axis 2. A displacement vector r in the xy plane is 34 m long and directed at angle ? = 44° as shown below. Determine the x and y components of the vector. x component = y component=An athlete crosses a 28 meters wide river by swimming perpendicular to the water current at a speed of 1.1 m/s relative to the water. He reaches the opposite side at a distance of 42 meters downstream from his starting point. w = 28md = 42m vs = 1.1m/s How fast is the water in the river flowing with respect to the ground in m/s?
- A 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 and an acceleration of +12.5 m/s2. What are the (a) x and (b) y coordinates of the center of the circular path?A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.70 m, 3.70 m) with a velocity of –5.80 i^ m/s and an acceleration of +13.3 j^ m/s2. What are the (a) x and (b) y coordinates of the center of the circular path?A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates ( 4.80 m, 4.00 m) with a velocity of – 3.50 i^ m/s and an acceleration of + 10.9 j^ m/s2. What are the (a) x and (b) y coordinates of the center of the circular path?