You use a slingshot to launch a potato horizontally from the edge of a cliff with speed v0. The acceleration due to gravity is g. Take the o

Question

You use a slingshot to launch a potato horizontally from the edge of a cliff with speed v0. The acceleration due to gravity is g. Take the origin at the launch point. Suppose that y-axis is directed upward and speed v0 is in the x-direction. How long after you launch the potato has it moved as far horizontally from the launch point as it has moved vertically

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Thành Công 3 years 2021-09-05T14:42:43+00:00 1 Answers 273 views 0

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  1. lethu
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    2021-09-05T14:44:37+00:00
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    Answer:

    \displaystyle t=\frac{2v_o}{g}

    Explanation:

    Horizontal Launch

    When an object is launched horizontally at a speed vo, it describes a curved called parabola as the speed in the x-direction does not change and the speed in the y-direction increases with time because the gravity makes it return to the ground.

    The vertical distance the object (potato) travels downwards is:

    \displaystyle y=\frac{gt^2}{2}

    The horizontal distance is

    x=v_ot

    We need to find the time when both distances are equal, thus

    \displaystyle \frac{gt^2}{2}=v_ot

    Simplifying by t

    \displaystyle \frac{gt}{2}=v_o

    Solving for t

    \displaystyle \boxed{t=\frac{2v_o}{g}}

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