(6) An object is moving in the xy-coordinate plane. The components of the object's velocity are vx = 5 m/s and vy = (3t-6) m/s. The components of object's acceleration are ax = (t-7) m/s2 and ay = (4t - 2) m/$2. Which of the following vectors best represents the velocity and acceleration of the object at t=2s? Vx ax (A) VX ax (B) VX ax (C) Vx ax (D) VX ax (E) (7) A small particle starts from rest from the origin of an xy-coordinate system and travels in the xy-plane. Its acceleration in the x-direction is 2.0 m/s , and its acceleration in the y-direction is 1.0 m/s. What is the x- coordinate of the particle when its y-coordinate is 12 m? (A) 3.0 m (B) 6.0 m (C) 12 m (D) 24 m (E) 48 mQuestion Proof/Work/Explanation (1) A person wants to paddle a canoe from point to point, which is directly across a river from point, as shown in the figure above. The water in the river flows at , and the person can paddle the canoe at in still water. Which of the following vectors best represents the appropriate heading for the canoe if it is to land at point Y? Y 5 m/s X (A) (B) (C) (D) (E (2) Student 1 is standing on a cart holding a small stone, while student 2 is standing at rest on the ground, as shown in the figure above. The cart is moving at a constant speed v in the +x-direction, as indicated by the coordinate system shown. Student 1 drops the stone precisely when passing student 2. Which of the following best represents the path of the falling stone relative to student 1 and the path of the falling stone relative to student 2 ? LO- Student 1 Student 2 Page 3 of 11 (3) A train is traveling at a constant speed eastward, and the velocity vector Vr is shown in the diagram above. The velocity vector @Gof a cyclist moving at a direction of 150 east of north is also shown. Which of the following vectors could represent the velocity of the cyclist as seen by someone on the train? 15% N Cyclist E Train Note: Figure not drawn to scale. Vos = Com +Vr V A. B. C. D (4) At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant. What is the speed of the pilot relative to the ground? (A) v1 + v2 (B) v1 - V2 (C) v2 - V1 (D)v1 - vz (E) Vuj + vzIII. Projectile Motion Question Proof/Work/Explanation A. Projectile Motion Introduction (1) A small sphere is thrown through the air and follows the parabolic path shown in the figure. Point is the highest point the sphere reaches. Assuming air resistance is negligible, which of the following claims is true of the sphere while it is in motion? (A) The vertical component of the sphere's velocity is at a maximum at point . (B) The horizontal component of the sphere's velocity is zero at point. C) The acceleration of the sphere is constant. (D) The sphere's speed is constant. (E) The displacement of the sphere is zero at point . (2) A ball is thrown and follows a parabolic path, as shown above. Air friction is negligible. Point @ is the highest point on the path. Which of the following best indicates the direction of the acceleration, if any, of the ball at point Q? downward (3] A ball is struck at time & = 0 and follows the parabolic path shown in the diagram above. The following graphs show quantities possibly associated with the motion as a function of time t. Assume that air resistance is negligible and that the positive directions are upward and to the right. A A. B D. O E. i. Which graph represents the horizontal component of the velocity of the ball? D ii. Which graph represents the vertical component of the velocity of the ball?E Page 5 of 11 (4) A rock is thrown from the edge of a cliff with an initial velocity vo at an angle 0 with the horizontal as shown above. Point P is the highest point in the rock's trajectory and point @ is level with the starting point. Assume air resistance is negligible. Uo Horizontal speed Vertical Speed Acceleration A VoCOSO 0 B. 0 C. VoCOSO D. ToCose Vasil VoCOSO i. Which of the following correctly describes the horizontal and vertical speeds and the acceleration of the rock at point P? A H. Which of the following correctly describes the horizontal and vertical speeds and the acceleration of the rock at point Q 7 B (5) An object is launched with the velocity shown. The horizontal and vertical components and , respectively, of the initial velocity are also shown. If air resistance is negligible, which of the following best shows ax and ay when the object reaches the highest point in its trajectory? Vo Vy Vx ax = 0 ay = downward