The gain of the potential energy by Tim is equal to the product of his mass , gravitational acceleration and the height he climbed vetically along the rope.
His mass =64.3 Kg, The gravitational acceleration = 9.8m/s and the height he climbed =3meter.
Therefore the potential energy Tim gained in this deed =64.3*9.8*3 J=1890.42 J
To move any object moves against the force of gravity, a force equal to mass of the object (m) multiplied by the acceleration due to gravity (g) is required. When the distance thus moved is s, the total energy used for moving the object is force multiplied by the distance s. The object thus moved up has acquired this additional energy used in raising it. This energy stored in an object because of change in its position is called potential energy. From the above discussion it is clear that potential energy gained from any vertical upward movement can be calculated using following formula.
Potential energy gained = m*g*s
m = 64.3 kg
g = 9.8 m/s^2
s = 3 m
Potential energy gained by Tim = m*g*s = 64.3*9.8*3 = 1890.42 J
Potential energy gained buy Tim is 1890.42 J.