m = mass of the person bouncing = 78 kg
k = spring constant of the bathroom scale = 1.5 x 10⁶ N/m
v = maximum velocity of the person
A = maximum compression of the spring of scale = 0.115 cm = 0.00115 m
h = height gained at maximum speed = A = 0.00115 m
Using conservation of energy
spring potential energy = kinetic energy + gravitational potential energy
(0.5) k A² = (0.5) m v² + m g h
k A² = m v² + 2 m g h
(1.5 x 10⁶) (0.00115)² = (78) v² + 2 (78) (9.8) (0.00115)
v = 0.0538 m/s
