a. 10 meters up:
At a height of 10 meters above the pool, the diver has potential energy given by:
PE = mgh
PE = (80 kg)(9.81 m/s²)(10 m)
PE = 7,848 J
Since the diver is at rest, their kinetic energy is zero.
b. 5 meters up:
At a height of 5 meters above the pool, the diver has potential energy given by:
PE = mgh
PE = (80 kg)(9.81 m/s²)(5 m)
PE = 3,924 J
Assuming no external forces act on the diver, the conservation of energy principle tells us that the total energy (potential energy + kinetic energy) is constant. Therefore, if we know the potential energy at one height, we can use it to find the kinetic energy at another height.
The potential energy at 5 meters is half the potential energy at 10 meters, so the remaining energy is kinetic. Therefore, at a height of 5 meters above the pool, the diver has kinetic energy given by:
KE = PE/2
KE = 7,848 J/2
KE = 3,924 J
c. 0 meters up:
When the diver reaches the pool surface, they are at a height of 0 meters above the pool. At this point, all of the potential energy has been converted to kinetic energy.
Using the conservation of energy principle, we can find the kinetic energy at 0 meters:
PE = KE
mgh = (1/2)mv²
v² = 2gh
v = sqrt(2gh)
v = sqrt(2 x 9.81 m/s² x 10 m)
v = 14.0 m/s
The kinetic energy at 0 meters is given by:
KE = (1/2)mv²
KE = (1/2)(80 kg)(14.0 m/s)²
KE = 15,680 J