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10 November, 04:31

A wide receiver catches a ball and begins to run for the endzone following a path defined by. A defensive player chases the receiver as soon as he starts running following a path defined by. Write parametric equations for the path of each player. a. receiver: defensive: c. receiver: defensive: b. receiver: defensive: d. receiver: defensive:

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  1. 10 November, 06:43
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    Receiver path:

    x-5 = t (0)

    y-50 = - 10t

    defender path:

    x-10 = - 0.9t

    y-54 = -10.72t

    Yes, he will reach the goal line (y = 0) before the defensive player catches him.

    Step-by-step explanation:

    Vector equation: (x-x1, y-y1) = t (a1, a2)

    Horizontal component : x-x1 = ta1

    Vertical component: y-y1 = ta2

    (x-5, y-50) = t (0, - 10)

    x-5 = t (0)

    y-50 = t (-10)

    Parametric equation for the receiver path:

    x-5 = t (0)

    y-50 = - 10t

    (x - 10, y - 54) = t (-0.9, - 10.72)

    x - 10 = t (-0.9)

    y - 54 = t (-10.72)

    Parametric equation for the defender path:

    x-10 = - 0.9t

    y-54 = -10.72t

    At the 50yard line, using the receiver parametric equation for vertical component:

    y-50 = - 10t

    At y = 50

    50-50 = - 10t

    0 = - 10t

    t = 0/-10 = 0

    At y = 0

    0-50 = - 10t

    t = - 50/-10 = 5

    Defender at y = 50

    y-54 = -10.72t

    50-54 = -10.72t

    t = - 4/-10.72 = 0.37

    at y = 0

    0-54 = -10.72t

    t = - 54/-10.72 = 5.04

    t of receiver < t of defender

    Since time of receiver at y=0 is less than time of defender, he will reach the goal line (y = 0) before the defensive player catches him.
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