Question

A ball is dropped 5 meters from rest. Using conservation of energy, what is the final velocity of the ball? a.) 5.39 m/s b.) 4.45 m/s c.) 9.90 m/s d.) 1.23 m/s e.) None of the above

Answer 1

Answer:

The final velocity of the ball, v = 9.9 m/s

Explanation:

It is given that,

A ball is dropped 5 meters from rest, h = 5 meters

We need to find the final velocity of the ball. It can be calculated using the conservation of energy as :

$KE_i+KE_f=PE_i+PE_f$

Initial kinetic energy, $KE_i=0\ (rest)$

Final kinetic energy, $KE_f=\dfrac{1}{2}mv^2$

Initial potential energy, $PE_i=mgh$

Final potential energy, $PE_f=0$ (at ground, h = 0)

$\dfrac{1}{2}mv^2=mgh$

$v=\sqrt{2gh}$

$v=\sqrt{2\times 9.8\ m/s^2\times 5\ m}$

v = 9.89 m/s

or

v = 9.9 m/s

So, the final velocity of the ball is 9.9 m/s. Hence, this is the required solution.