An open box of height $1 m$ is placed near a $2 m$ high table as shown. Marble rolling on the table leaves the table and are collected in the box $u_{max}$ and $u_{min}$ are the minimum and maximum values of velocity of marbles to fall into the box. Find the value of $u_{max} - u_{min}$ $(i n m / s)$

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Solution

Time when it is at the interact of the bucket
writing equation in verticle directions
$S = u t + \frac{1}{2} g t^{2}$
$1 = 0 + \frac{1}{2} g t^{2}$
$t = \frac{1}{\sqrt{5}}$
for horizontal direction
$u_{min} \Rightarrow u_{min} \times t = \sqrt{5}$
${u_{\min }} \times \dfrac{1}{{\sqrt 5 }} = \sqrt 5 \Rightarrow {u
_{\min }}\, = 5\,m/s$
for $u_{max}$
$u_{max} \Rightarrow u_{max} \times t = 2 \sqrt{5}$
$u_{max} \times \frac{1}{\sqrt{5}} = 2 \sqrt{5} \Rightarrow u_{max} = 10 m / s$
$u_{max} - u_{min} = 10 - 5 = 5 m / s$

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An open box of height 1m is placed near a 2m high table as shown. Marble rolling on the table leaves the table and are collected in the box umax and umin are the minimum and maximum values of velocity of marbles to fall into the box. Find the value of umax−umin (inm/s)