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3 October, 23:19

A car heading north collides at an intersection with a truck of the same mass as the car heading east. If they lock together and travel at 28 m/s at 27° north of east just after the collision, how fast was the car initially traveling? Assume that any other unbalanced forces are negligible.

A. 25 m/s

B. 13 m/s

C. 19 m/s

D. 50 m/s

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  1. 4 October, 01:46
    0
    Initial speed of car = 25 m/s north direction

    correct option is A. 25 m/s

    Explanation:

    given data

    Final velocity of both = 28 m/s at 27 degrees north of east

    to find out

    how fast was the car initially traveling

    solution

    we consider both vehicle have same mass

    mass of car m1 = mass of truck m2

    so we will apply here conservation of momentum law

    m1 * u1 j + m2 * u2 i = (m1 + m2) * (v cosθ i + v sinθ j) ... 1

    here m is mass and u is initial velocity and v is final velocity

    m * u1 j + m * u2 i = (2m) * (28 * cos27 i + 28 * sin27 j)

    u2 i + u1 j = 2 (24.94 i + 12.71 j)

    u2 i + u1 j = 49.88 i + 25.42 j

    so compare both side we get

    Initial speed of car u1 = 25.42 m/s north direction
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