(c) The potential energy at A is the same as the kinetic energy at B. So
m g h = 1/2 m v²
where m is the mass of the object at the end of the pendulum, g is the magnitude of the acceleration due to gravity, h is the height of the object at point A relative to B, and v is the object's maximum speed. So
(3.8 kg) (9.80 m/s²) h = 140 J
h = (140 J) / ((3.8 kg) (9.80 m/s²))
h ≈ 3.8 m
(f) You know the kinetic energy at B, so just solve for v :
140 J = 1/2 (3.8 kg) v²
v² = (280 J) / (3.8 kg)
v² ≈ 73.684 m²/s²
v ≈ 8.6 m/s
