A train travels due north in a straight line with a constant speed of 100 m/s. Another train leaves a station 2,881 m away traveling on the

Question

A train travels due north in a straight line with a constant speed of 100 m/s. Another train leaves a station 2,881 m away traveling on the same track, but traveling due south with a constant speed of 136 m/s. At what position will the trains collide? Round to the nearest whole number.

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Thanh Thu 3 years 2021-08-02T00:59:02+00:00 1 Answers 14 views 0

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    2021-08-02T01:00:47+00:00

    Answer:

    The trains will collide at a distance 1660 m from the station

    Explanation:

    Let the train traveling due north with a constant speed of 100 m/s be Train A.

    Let the train traveling due south with a constant speed of 136 m/s be Train B.

    From the question, Train B leaves a station 2,881 m away (that is 2,881 m away from Train A position).

    Hence, the two trains would have traveled a total distance of 2,881 m by the time they collide.

    ∴ If train A has covered a distance x m by the time of collision, then train B would have traveled (2881 - x) m.

    Also,

    At the position where the trains will collide, the two trains must have traveled for equal time, t.

    That is, At the point of collision,

    t_{A} = t_{B}

    t_{A} is the time spent by train A

    t_{B} is the time spent by train B

    From,

    Velocity = \frac{Distance }{Time }\\

    Time = \frac{Distance}{Velocity}

    Since the time spent by the two trains is equal,

    Then,

    \frac{Distance_{A} }{Velocity_{A} }  = \frac{Distance_{B} }{Velocity_{B} }

    {Distance_{A} = x m

    {Distance_{B} = 2881 - x m

    {Velocity_{A} = 100 m/s

    {Velocity_{B} = 136 m/s

    Hence,

    \frac{x}{100} = \frac{2881 - x}{136}

    136(x) = 100(2881 - x)\\136x = 288100 - 100x\\136x + 100x = 288100\\236x = 288100\\x = \frac{288100}{236} \\x = 1220.76m\\

    x≅ 1,221 m

    This is the distance covered by train A by the time of collision.

    Hence, Train B would have covered (2881 – 1221)m = 1660 m

    Train B would have covered 1660 m by the time of collision

    Since it is train B that leaves a station,

    ∴ The trains will collide at a distance 1660 m from the station.

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