Question

A 5.00 kg pendulum swings back and forth. At the top of its arc, it reaches a height of 0.36 m. What is the velocity of the pendulum at the bottom of the arc?
0m/s
2.7m/s
7.2m/s

Answer 1

Tools we'll use:

--     Gravitational potential energy = (mass) x (gravity) x (height)

--     Kinetic energy (of a moving object) = (1/2) (mass) x (speed)²

When the pendulum is at the top of its swing,
its potential energy is

                             (mass) x (gravity) x (height)

                         =  (5 kg) x (9.8 m/s²) x (0.36 m)

                         =      (5 x 9.8 x 0.36)        joules

                         =            17.64 joules .

Energy is conserved ... it doesn't appear or disappear ...
so that number is exactly the kinetic energy the pendulum
has at the bottom of the swing, only now, it's kinetic energy:

                   17.64 joules  =  (1/2) x (mass) x (speed)²

                   17.64 joules  =  (1/2) x (5 kg) x (speed)²

Divide each side by 2.5 kg:

                   17.64 joules / 2.5 kg  =  speed²

Write out the units of joules:

                   17.64 kg-m²/s²  /  2.5 kg  =  speed²

                   (17.64 / 2.5) (m²/s²)  =  speed²

                       7.056 m²/s²  =  speed²

Take the square root
of each side:              Speed = √(7.056 m²/s²)

                                           =    2.656 m/s .

Looking through the choices, we're overjoyed to see
that one if them is  ' 2.7 m/s '.  Surely that's IT !
_______________________________

Note:
The question asked for the pendulum's 'velocity', but our (my) calculation
only yielded the speed.

In order to describe a velocity, the direction of the motion must be known,
and the question doesn't give any information on exactly how the pendulum
is hanging, and how it's swinging. 

We know that at the bottom of its swing, the motion is completely horizontal,
but we have no clue as to what direction.  So all we can discuss is its speed.