Collision at an Angle Two cars, both of mass , collide and stick together. Prior to the collision, one car had been traveling north at speed , while the second was traveling at speed at an angle south of east (as indicated in the figure). After the collision, the two-car system travels at speed at an angle east of north. Part A Find the speed of the joined cars after the collision. Hint A.1 Determine the conserved quantities Which of the following statements is true for the collision described? ANSWER: Momentum is conserved but kinetic energy is not conserved. Kinetic energy is conserved but momentum is not conserved. Both kinetic energy and momentum are conserved. Neither kinetic energy nor momentum is conserved. Correct Apply conservation of momentum: . Find both components (north and east) of the initial momentum using the information in the problem introduction. The magnitude of is equal to the magnitude of the momentum vector for the two-car system after the collision: . Hint A.2 The component of the final velocity in the east-west direction Find the component of in the east-west direction.
Hint A.2.1 Find the east-west component of the initial momentum What is , the magnitude of the total momentum of the two cars in the east-west direction? (Take eastward to be positive, westward negative.) Express your answer in terms of , , and . ANSWER: = Correct Now use the conservation of momentum equation to find . Express your answer in terms of and . ANSWER: (east-west) = Correct Hint A.3 Find the north-south component of the final momentum Find the component of in the north-south direction. Hint A.3.1 Find the north-south component of the initial momentum What is the magnitude of the total momentum of the two cars in the north-south direction? (Take northward to be positive, southward negative). Express your answer in terms of , , and . ANSWER: = Correct Express your answer in terms of and . ANSWER: (north-south) = Correct Hint A.4 Math help Let be the east-west component of , and the north-south component. Then . You will also need to use the following trignometric identity when you evaluate the right-hand side of the above equation in terms of and : . Express your answer in terms of and .
ANSWER: = Correct Part B What is the angle with respect to north made by the velocity vector of the two cars after the collision? Hint B.1 A formula for Let be the east-west component of , and the north-south component. Then , since the angle asked for is the angle east of north. Express your answer in terms of . Your answer should contain an inverse trigonometric function. ANSWER: = Correct A Ball Hits a Wall Elastically A ball of mass moving with velocity strikes a vertical wall. The angle between the ball's initial velocity
This is the end of the preview. Sign up to
access the rest of the document.