Question

What is the speed u of the object at the height of (1/2)hmax? Express your answer in terms of v and g. Use three significant figures in the numeric coefficient.

Answer 1

The speed u of the object at the height of (1/2) hmax is $0.707$ $v_{i}$.

Explanation:

At a height that is half of the maximum height, the object will have only half of its initial kinetic energy, the rest half is converted to potential energy at this point. So,

                              $1 / 2 m v^{2} _{i} = m (v_{mid})^{2} }$

                                  $v_{mid} = \frac{v}{\sqrt{2} }$

                                $v_{mid} =$   $0.707$ $v_{i}$.

The speed u of the object at the height of (1/2) hmax is $0.707$ $v_{i}$.