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20 August, 15:37

A car of mass 998 kilograms moving in the positive y-axis at a speed of 20 meters/second collides on ice with another car of mass 1,200 kilograms moving in the negative x direction with a speed of 17 meters/second. After the collision, the cars stick and move together. What is the total momentum in the x direction before the collision?

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  1. 20 August, 17:44
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    Let’s determine the initial momentum of each car.

    #1 = 998 * 20 = 19,960

    #2 = 1200 * 17 = 20,400

    This is this is total momentum in the x direction before the collision. B is the correct answer. Since momentum is conserved in both directions, this will be total momentum is the x direction after the collision. To prove that this is true, let’s determine the magnitude and direction of the total momentum after the collision.

    Since the y axis and the x axis are perpendicular to each other, use the following equation to determine the magnitude of their final momentum.

    Final = √ (x^2 + y^2) = √ (20,400^2 + 19,960^2) = √814,561,600

    This is approximately 28,541. To determine the x component, we need to determine the angle of the final momentum. Use the following equation.

    Tan θ = y/x = 19,960/20,400 = 499/510

    θ = tan^-1 (499/510)

    The angle is approximately 43.85˚ counter clockwise from the negative x axis. To determine the x component, multiply the final momentum by the cosine of the angle.

    x = √814,561,600 * cos (tan^-1 (499/510) = 20,400
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