Apply conservation of energy; the pendulum's maximum potential energy (at the highest point of its motion) equals the maximum kinetic energy (at the lowest point of its motion):
Max PE = Max KE
We will calculate the max PE, ie the potential energy after that ball is lifted up:
Max PE = mgh
PE is the potential energy, m is the ball's mass, g is acceleration due to earth's gravity, and h is the height.
Given values:
m = 2kg
g = 9.81m/s²
h = 1.5m
Plug in the values and solve for Max PE:
Max PE = 2(9.81)(1.5)
Max PE = 29.43J
The ball's kinetic energy is given by:
KE = 0.5mv²
We know the ball's velocity is greatest when it attains Max KE, and the max KE equals the Max PE:
Max KE = Max PE = 29.43J = 0.5mv²
Given values:
m = 2kg
Now plug in and solve for v:
2v² = 58.86
v = 5.425
v = 5.4m/s
