Part B:
Potential energy (P) can be calculated by
P = mgh = 51 * 9.807 * 10.8 = 5401.6956 J
Potential energy (P.E) = 5401.6956 J
where m = mass of diver in kg; g = gravitational force due to earth = 9.807 m/s2 ; h = height (distance) between the apex and water surface = 10.8 m.
now this is K.E before striking the surface = 1/2 m v2
set the potential energy (P.E) equal to kinetic energy (K.E):
5401.6956 J = 1/2 (51)(v^2)
v = 14.5544220084 m/s
Speed = 14.5 m/s (3 significant figures)
Part C:
YES. The diver does work upon entering water. While entering into the water, the kinetic energy is reduced due to water resistance (viscocity, surface tension etc). Hence work must be done against water resistance. work done= change in KE.
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