Question

What is the velocity of the object when the potential energy equals the kinetic energy if it is induced into free fall at a height of $20m$ from rest?

• A. $8m/s$
• B. $11m/s$
• C. $14m/s$
• D. $17m/s$
• E. There is not enough information to determine the velocity

Answer 1

The correct option is C $14m/s$

Let the velocity of object be $v$ at the instant the kinetic energy equals the potential energy.

Total energy of the object initially $T.E_i=mgh$ where $h=20$ m

Using conservation of total energy : $T.E_i=T.E_f$

$\therefore$ $mgh=P.E+K.E$

OR $mgh=2K.E$

OR $mgh=2\times \frac{m{v}^2}{2}$ $⟹v=\sqrt{gh}$

$\therefore$ $v=\sqrt{9.8\times 20}=14$ $m/s$