A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m/s over the hill. The canon is located at a distance of 800m from the foot of hill and can be moved on the ground at a speed of 2 m/s; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill ? Take g =10 m/s2.

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    Answered by

    Vishal Baghel | Contributor-Level 10

    3 months ago

    This is a Long Answer Type Question as classified in NCERT Exemplar

    Explanation- speed of jackets = 125m/s

    Height of hill = 500m

    To cross the hill vertical component of velocity should be grater than this value uy= 2 g h

    = 2 * 10 * 500 = 100 m / s

    So u2= ux2+uy2

    Horizontal component of initial velocity ux = u 2 - u y 2 = 125 2 - 100 2 = 75 m / s

    Time taken to reach the top of hill t= 2 h g = 2 * 500 10 = 10 s

    Time taken to reach the ground in 10 sec = 75 (10)= 750m

    Distance through which the canon has to be moved =800-750=50m

    Speed with which canon can move = 2m/s

    Time taken canon = 50/2= 25s

    Total time t= 25+10+10= 45s

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