Apendulum is used in a large clock. the pendulum has a mass of 2kg. if the pendulum is moving at a speed of 4.1m/s when it reaches the lowest point on its path, what is the maximum length of the pendulum?

There's no way to calculate the length of the pendulum
with the given information.

The only thing we can calculate is the total energy in the pendulum.

When the pendulum is at the bottom of its swing, ALL of its energy
is kinetic.

       Kinetic energy = (1/2) x (mass) x (speed)²

                             = (1/2) x  (2 kg) x (4.1 m/s)²

                             =    4.1  kg-m²/sec²

                             =    4.1 Joules .

In principle, we can also calculate how HIGH the 'bob' is at the end of
its swing, because now we know how much total energy the pendulum
has, and at the ends of the swing, the energy is all potential.

       Potential energy  =  (mass) x (gravity) x (height)

               4.1 J  =  (2 kg) x (9.8 m/s²) x (height)

               Height  =  (4.1 kg-m²/s²) / (19.6 kg-m/s²)

                           =    0.209 meter high

and that's as far as we can go.  None of this points us toward
calculating the length of the pendulum.

Dis the