First slide

Release from certain height

Question

An object is projected vertically upward with velocity u from the bottom of a tower of height H. At the same time another object is released from rest from the top of the tower. They are moving along the same vertical line. The objects will collide in air if

Difficult

A

$u>\sqrt{\frac{gH}{8}}$ $u < \sqrt{\frac{g H}{2}}$
B

$u>\sqrt{\frac{gH}{2}}$ $u > \sqrt{\frac{g H}{2}}$
C

$\sqrt{\frac{g H}{2}} > u > \sqrt{g H}$
D

$u = \frac{1}{2} \sqrt{g H}$ $u>\frac{1}{4}\sqrt{gH}$

Solution

For the object released from the top of a tower , $T_{1} = \sqrt{\frac{2 H}{g}}$
For the object projected vertically upward , $T_{2} = \frac{2 u}{g}$
The objects will collide if $T_{2} > T_{1}$
that is if , u $> \sqrt{\frac{g H}{2}}$

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