Question

EXAMPLE 6.8 Collision at an Intersection GOAL Analyze a two-dimensional inelastic collision. 25.0 m/s +20,0 m/s A top view of a perfectly inelastic collision between a car and a van. PROBLEM A car with mass 1.50 x 103 kg traveling east at a spegd of 25.0 m/s collides at an intersection with a 2.50 x 10 kg van traveling north at a speed of 20.0 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 STRATEGY Use conservation of momentum in two dimensions. (Kinetic energy is not conserved.) Choose coordinates as in the figure. Before the collision, the only object having momentum in the x- direction is the car, while the van carries all the momentum in the y-direction. After the totally inelastic collision, both vehicles move together at some common speed tf and angle θ. Solve for these two unknowns, using the two components of the conservation of momentum equation SOLUTION Find the x-components of the initial and final total momenta. mcar(1.50 x 103 kg)(25.0 m/s) -3.75 x 104 kg. m/s cos θ (4.00 103 kg)y, cos θ Type here to search

Answer 1

Practice it: conserving momentum along x: (1510) (22.5) = (1510 + 2540) v_f x = > v_f x = 8.39 m/s conserving momentum along y: (2540) (18.2) = (1510 + 2540) v_f y = > v_f y = 11.41 m/s therefore Vertical-bar v_f Vertical-bar = squareroot v_f x^2 + v_fy^2 = 14.2 m/s theta = tan^-1 (v_f y/v_f x) = 53.67 degree