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Motion in Two Dimensions: Position, Velocity, and Acceleration Vectors

This problem set covers various concepts of motion in two dimensions, including position, velocity, and acceleration vectors. Topics include projectile motion, uniform circular motion, tangential and radial acceleration, and relative velocity and acceleration.

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Motion in Two Dimensions: Position, Velocity, and Acceleration Vectors

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  1. Position, velocity, acceleration vectors Average & Instantaneous Velocity Average & Instantaneous Acceleration Two Dimensional Motion with Constant Acceleration (Kinematics) Projectile Motion (Free Fall) Uniform Circular Motion Tangential and Radial Acceleration Relative Velocity and Relative Acceleration Physics 111 Practice Problem Statements 03Motion in Two DimensionsSJ 8th Ed.: Ch. 4.1 – 4.4 Contents: 4-3E, 4-5E, 4-12E, 4-13E*, 4-28P, 4-29E*, 4-33P*, 4-42E, 4-44E, 4-45E, 4-49P Extra: 4-25P (Range)

  2. Problem 4 - 3E: The position vector for a proton is initially r1= 5.0 i - 6.0 j + 2.0 k and then later is r2= -2.0 i + 6.0 j + 2.0 k , all in meters. (a) What is the proton's displacement vector, and (b) to what plane is that vector parallel?

  3. Problem 4 - 5E: A train moving at a constant speed of 60.0 km/h moves east for 40.0 min, then in a direction 50.0° east of north for 20.0 min, and finally west for 50.0 min. What is the average velocity of the train during this trip?

  4. Problem 4-12E: If An iceboat sails across the surface of a frozen lake with constant acceleration produced by the wind. At a certain instant the boat's velocity is (6.30 i - 8.42 j) m/s. Three seconds later, because of a wind shift, the boat is instantaneously at rest. What is its average acceleration for this 3 s interval?

  5. Problem 4-13E*: A particle leaves the origin with an initial velocity v = (3.00 i) m/s and a constant acceleration a = (-1.00 i - 0.500 j) m/s2. When the particle reaches its maximum x coordinate, what are (a) its velocity and (b) its position vector?

  6. Problem 4- 28P: You throw a ball toward a wall with a speed of 25.0 m/s and at an angle of 40.0° above the horizontal (Fig. 4-35). The wall is 22.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? (b) What are the horizontal and vertical components of its velocity as it hits the wall? (c) When it hits, has it passed the highest point on its trajectory?

  7. Problem 4- 29E*: A ball is shot from the ground into the air. At a height of 9.1 m, its velocity is observed to be v = 7.6 i + 6.1 j in meters per second ( i horizontal, upward j). (a) To what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are (c) the magnitude and (d) the direction of the ball's velocity just before it hits the ground?

  8. Problem 4- 33P*: A certain airplane has a speed of 290.0 km/h and is diving at an angle of 30.0° below the horizontal when the pilot releases a radar decoy (Fig. 4-36). The horizontal distance between the release point and the point where the decoy strikes the ground is 700 m. (a) How long is the decoy in the air? (b) How high was the released point?

  9. Problem 4- 42E: What is the magnitude of the acceleration of a sprinter running at 10 m/s when rounding a turn with a radius of 25 m?

  10. Problem 4- 44E: A rotating fan completes 1200 revolutions every minute. Consider the tip of a blade, at a radius of 0.15 m. (a) Through what distance does the tip move in one revolution? What are (b) the tip's speed and (c) the magnitude of its acceleration? (d) What is the period of the motion?

  11. Problem 4- 45E: An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. (a) What is the astronaut's speed if the centripetal acceleration has a magnitude of 7.0g? (b) How many revolutions per minute are required to produce this acceleration? (c) What is the period of the motion?

  12. Problem 4- 49P: A carnival Ferris wheel has a 15 m radius and completes five turns about its horizontal axis every minute. (a) What is the period of the motion? What is the centripetal acceleration of a passenger at (b) the highest point and (c) the lowest point, assuming the passenger is at a 15 m radius?

  13. Problem 4- 25P: A rifle that shoots bullets at 460 m/s is to be aimed at a target 45.7 m away and level with the rifle. How high above the target must the rifle barrel be pointed so that the bullet hits the target?

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