A rock is thrown upwards and has a max altitude of 40 m. What was its initial velocity?

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A rock is thrown upwards and has a max altitude of 40 m. What was its initial velocity?

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Hải Đăng 4 years 2021-07-19T05:28:42+00:00 1 Answers 7 views 0

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  1. Latifah
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    2021-07-19T05:30:32+00:00
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    Recall the formula,

    {v_f}^2-{v_i}^2=2a\Delta x

    where v_i and v_f are the rock’s initial and final velocities, respectively; a is its acceleration; and \Delta x is the displacement it undergoes.

    At any point during its motion, the rock is subject to gravity, so a=-g, where g=9.80\frac{\rm m}{\mathrm s^2}. At its maximum height, the rock has zero vertical velocity, and if we take its starting height to be the origin, we have \Delta x=x_{\rm max}.

    So,

    0^2-{v_i}^2=-2gx_{\rm max}\implies-{v_i}^2=-2\left(9.80\dfrac{\rm m}{\mathrm s^2}\right)(40\,\mathrm m\implies\boxed{v_i=28\dfrac{\rm m}{\rm s}}

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