Kinematics in Two-Dimensions 8.01 W02D2Concept Q.: 2-Dim Kinematics A person simultaneously throws two objects in the air. The objects leave the person’s hands at different angles and travel along the parabolic trajectories indicated by A and B in the figure below. Which of the following statements best describes the motion of the two objects? 1. The object moving along the trajectory A hits the ground before the object moving along the trajectory B. 2. The object moving along the higher trajectory A hits the ground after the object moving along the lower trajectory B. 3. Both objects hit the ground at the same time. 4. There is not enough information specified in order to determine which object hits the ground first.Table Problem: Baseball A batter hits a baseball into the air with an initial speed, v0 = 50 m/s , and makes an angle θ0 = 30o with respect to the horizontal. How far does the ball travel if it is caught at exactly the same height that it is hit from? When the ball is in flight, ignore all forces acting on the ball except for gravitation. Let g = 9.8 m/s2.Table Problem: Law of Addition of Velocities Suppose two cars, Car 1, and Car 2, are traveling along roads that are perpendicular to each other. Reference Frame A is at rest with respect to the ground. Reference Frame B is at rest with respect to Car 1. Choose unit vectors such that Car 1 is moving in the positive y-direction, and Car 2 is moving in the positive x-direction in reference Frame A. a) What is the vector description of the velocity of Car 2 in Reference Frame B? b) What is the magnitude of the velocity of Car 2 as observed in Reference Frame B? c) What angle does the velocity of Car 2 make with respect to the positive x-direction as observed in Reference Frame B?Demo: Relative Motion Gun A7 Video Link: http://tsgphysics.mit.edu/front/index.php?page=demo.php?letnum=A%207&show=0Table Problem: Softball A softball is hit over a third baseman’s head. The third baseman, as soon as the ball is hit, turns around and runs straight backwards a constant speed of 7 m/s for a time interval 2 s and catches the ball at the same height it left the bat. The third baseman was initially a distance 18 m from home plate. What was the initial speed and angle of the softball when it left the bat?Non-Closed OrbitConcept Question Consider the path of a ball moving along a path through the air under the action of the gravitational force. You may neglect the effects of air friction. As it reaches the highest point in its arc, which of the following statement is true? 1) The magnitudes of the velocity and acceleration are zero. 2) The magnitude of the velocity is at a minimum but not equal to zero. 3) The magnitude of the velocity is equal to zero, and the magnitude of the acceleration is constant and not equal to zero. 4) The magnitude of the velocity is at a minimum but not equal to zero and the magnitude of the acceleration is zero. 5) Neither the magnitudes of acceleration or velocity has yet attained its minimum value.Source: Geo-Prospecting Mechanics by Landau and Liftshitz. http://www.dmtcalaska.org/exploration/ISU/unit3/u3lesson2.htmlWorked Example: Stuffed Animal and the Gun A stuffed animal is suspended at a height h above the ground. A physics demo instructor has set up a projectile gun a horizontal distance d away from the stuffed animal. The projectile is initially a height s above the ground. The demo instructor fires the projectile with an initial velocity of magnitude v0 just as the stuffed animal is released. Find the angle the projectile gun must be aimed in order for the projectile to strike the stuffed animal. Ignore air resistance.Demo: Stuffed Animal and Gun A6 Video Link http://tsgphysics.mit.edu/front/index.php?page=demo.php?letnum=A%207&show=0Concept Q.: 2-dim kinematics An object moves along a parabolic orbit under the influence of gravity. At each point along the orbit, 1. the magnitude of the velocity can be determined from the slope of the tangent line to the graph of y vs. x but not the direction. 2. the magnitude and direction of the velocity can be determined from the slope of the tangent line to the graph of y vs. x. 3. neither the magnitude nor the direction of the velocity cannot be determined from the slope of the tangent line to the graph of y vs. x. 4. the direction of the velocity can be determined from the slope of the tangent line to the graph of y vs. x but not the
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