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Math Help - Mechanics question - newton's laws, please help :(?

  1. #1
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    Mechanics question - newton's laws, please help :(?

    a heavy sphere is thrown 45 degrees upwards. it spends twice as long descending as ascending, because it's been thrown off a 30-metre-high cliff. it then hits the ground, and with each bounce loses 80% of its energy. will the ball hit someone standing 70metres from the cliff?
    assume g = 10 m/s/s

    this is all the question says. i think i've worked out the initial speed, but i'm not sure
    i am also assuming no air resistance, each time the ball hits the ground the collision is elastic, and that the person standing 70m away is infinitely tall, so that the ball cannot bounce over

    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by cassius View Post
    a heavy sphere is thrown 45 degrees upwards. it spends twice as long descending as ascending, because it's been thrown off a 30-metre-high cliff. it then hits the ground, and with each bounce loses 80% of its energy. will the ball hit someone standing 70metres from the cliff?
    assume g = 10 m/s/s

    this is all the question says. i think i've worked out the initial speed, but i'm not sure
    i am also assuming no air resistance, each time the ball hits the ground the collision is elastic, and that the person standing 70m away is infinitely tall, so that the ball cannot bounce over

    thanks
    As far as I can see in order to do this will require that you make some assumptions about what is happening at each bounce, but these do not look reasonable.

    CB
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    this is all the question says. i think i've worked out the initial speed, but i'm not sure
    There are many ways to find initial velocity....I would like to see your way ...in case of an error ..it will be pointed out.. so its my request that you kindly post your attempt at initial velocity and get your concept cleared..
    _________________
    Here is a hint at the main punch of your question.


    After every collision the velocity will become  (\frac{1}{\sqrt(5)})th of its value just before collision

    Range of a projectile with velocity v angle \theta is given by

    R= \frac{v^2 sin(2\theta)}{g}

    When you will add the range it will be of the form

    R + R_1 +R_2+R_3+.......= R + \frac{{v_1}^2 sin(2\theta)}{g}+\frac{{v_2}^2 sin(2\theta)}{g}+\frac{{v_3}^2 sin(2\theta)}{g}+......

    \theta will remain same and would be greater than 45 degree in this case

    R + R_1 +R_2+R_3+.......= R + \frac{{v_1}^2 sin(2\theta)}{g}+\frac{{v_1}^2 sin(2\theta)}{5g}+\frac{{v_1}^2 sin(2\theta)}{5*5g}+......

    This will be an infinite GP the total sum of which is given by a/(1-r)

    R_{complete}= R + R_1 +R_2+R_3+.......= R + \frac{{v_1}^2 sin(2\theta)}{g(1-\frac{1}{5})}
    ______________________

    You wont need to consider a 1000 feet giant for this question


    Take Care
    Adarsh
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