A 1210kg car and 4880kg truck undergo a perfectly inelastic collision. Before th

Question

A 1210kg car and 4880kg truck undergo a perfectly inelastic collision. Before the collision, the car was traveling southward at 1.50m/s. and the truck westward at 8.25m/s. Find the velocity of the wreckage immediately after the collision. Enter the x and y components of the velocity separated by a comma. Assume that the positive x and y axes are directed eastward and northward, respectively. vx, vy =

Explanation / Answer

x and y momenta are separately conserved, so we have for x momentum: -8.25m/s * 4880kg = -(4880+1210) V cos(theta) = 6.6 Where 4880+1210=6090 kg is the combined mass of the wreck; V is the speed of the wreck, and theta is the angle V makes with the negative x axis, so that Vcos(theta) is the x component of motion for y momentum: -1210*1.5m/s = -6090Vsin(theta) or we have 6.6=Vcos(Theta) 0.29= Vsin(theta) divide the y equation by the x equation: =tan(theta) => theta = 2.51 degrees with respect to the negative x axis, or an angle of 182 degrees counterclockwise from the positive x axis use this value of theta in either equation to solve for V 0.29=Vsin2.51 =>V=6.621m/s V=6.621m/s

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