GOAL Analyze a two-dimensional inelastic collision.PROBLEM A car with mass 1.50 x 10³ kg traveling east at aspeed of 25.0 m/s collides at an intersection with a 2.50 x 10³kg van traveling north at a speed of 20.0 m/s, as shown in thefigure. Find the magnitude and direction of the velocity of thewreckage after the collision, assuming that the vehiclesundergo a perfectly inelastic collision (that is, they sticktogether) and assuming that friction between the vehicles andthe road can be neglected.SOLUTIONFind the x-components of the initialand final total momenta.STRATEGY Use conservation of momentum in twodimensions. (Kinetic energy is not conserved.) Choosecoordinates as in the figure. Before the collision, the onlyobject having momentum in the x-direction is the car, whilethe van carries all the momentum in the y-direction. After the totally inelastic collision, both vehicles movetogether at some common speed vf and angle 0. Solve for these two unknowns, using the two componentsof the conservation of momentum equation.A top view of a perfectly inelastic collision between a carand a van.Set the initial x-momentum equal tothe final x-momentum.Find the y-components of the initialand final total momenta.Set the initial y-momentum equal tothe final y-momentum.Divide Equation (2) by Equation (1)and solve for 0.ΣpximcarV car= 3.75 x 104 kg. m/sΣpxf = (mcar + mvan) vf cos 0 = (4.00 × 10³ kg) vf cos (ΣΡίγ(1) 3.75 x 104 kgtan 0=Ꮎ+25.0 m/s==(1.50 x 10³ kg)(25.0 m/s)mvan van= 5.00 x 104 kg. m/s=Σpfy = (mcar + mvan) vf sin 0 (4.00 x 10³ kg) vf sin 0(2) 5.00 x 104 kg · m/s = (4.00 × 10³ kg) vf sin 053.1°x+20.0 m/sm/s = (4.00 × 10³ kg) vf cos 0(2.50 x 10³ kg)(20.0 m/s)5.00 x 104 kg. m/s3.75 x 104 kg. m/s= 1.33 LEARN MOREVfxREMARKS It's also possible to first find the x- and y-components and Vfy of the resultant velocity.The magnitude and direction of the resultant velocity can then be found with the Pythagorean theorem, vf= √v 2-1Vfx² + Vfy and the inverse tangent function 0 tan-¹ (v/v). Setting up this alternate approach is asimple matter of substituting vfx = vf cos and vfy = vf sin 0 in Equations (1) and (2).QUESTION If the car and van had identical mass and speed, what would the resultant angle havebeen?ImagnitudedirectionPRACTICE ITUse the worked example above to help you solve this problem. A car with mass 1.55 x 10³ kg travelingeast at a speed of 20.8 m/s collides at an intersection with a 2.55 x 10³ kg van traveling north at a speedof 19.2 m/s, as shown in the figure. Find the magnitude and direction of the velocity of the wreckage afterthe collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together)and assuming that friction between the vehicles and the road can be neglected.m/s° counterclockwise from the +x-axisO=EXERCISEA 3.22 kg object initially moving in the positive x-direction with a velocity of +4.99 m/s collides with andsticks to a 2.23 kg object initially moving in the negative y-direction with a velocity of -2.56 m/s. Find thefinal components of velocity of the composite object. (Indicate the direction with the sign of your answer.)VfxVfym/sm/sHINTS:GETTING STARTED II'M STUCK!

The initial momentum in the x-direction is given by, pxi = mcarvcar pxi = (1.55 × 103 kg)(20.8 m/s)…

Use the worked example above to help you solve this problem. A car with mass 1.55 x 10³ kg traveling east at a speed of 20.8 m/s collides at an intersection with a 2.55 x 10³ kg van traveling north at a speed of 19.2 m/s, as shown in the figure. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together) and assuming that friction between the vehicles and the road can be neglected. m/s ° counterclockwise from the +x-axis magnitude direction

Use the worked example above to help you solve this problem. A car with mass 1.55 x 10³ kg traveling east at a speed of 20.8 m/s collides at an intersection with a 2.55 x 10³ kg van traveling north at a speed of 19.2 m/s, as shown in the figure. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together) and assuming that friction between the vehicles and the road can be neglected. m/s ° counterclockwise from the +x-axis magnitude direction

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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