The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.

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Solutions of Savchenko Problems in Physics
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    <h3 id="back-link"><a href="/#1.4">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.4.11.$ The body is dropped over the slab at a height $h$ from it. The slab moves vertically upwards at a speed of $u$. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.
    </p>

    <h3>Solution</h3>
    <p>
        <p>Let's move to the reference frame associated with the plate. At the initial moment of time, the relative velocity is $u$ and is directed downwards.</p>

From the law of conservation of energy, we find the velocity of the body $v$ at the moment before the impact

$$\frac{mv^2}{2} = \frac{mu^2}{2} + mgh$$

Where is the desired velocity

$$v = \sqrt{u^2+2gh}$$

In this inertial reference frame, after an elastic rebound, the relative velocity will only change direction.

A body thrown vertically will land after time

$$t = \frac{2v}{g}$$

Time sought:

$$\fbox{$t = \frac{2\sqrt{u^2 + 2gh}}{g}$}$$

    <h4>Answer</h4>
    <p>
        $$t = 2\sqrt{u^2/g^2 + 2h/g}$$
    </p>



    <p style="text-align: right; font-style: italic; font-size: 14;">   
      Aliaksandr Melnichenka<br>
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