Answer:
Kinetic energy of diver at 90% of the distance to the water is 9000 J
Explanation:
Let d is the distance between the position of the diver and surface of the pool.
Initially, the diver is at rest and only have potential energy which is equal to 10000 J.
As the diver dives towards the pool, its potential energy is converting into kinetic energy due to law of conservation of energy, as total energy of the system remains same.
Energy before diving = Energy during diving
(Potential Energy + Kinetic Energy) = (Kinetic Energy + Potential Energy)
When the diver reaches 90% of the distance to the water, its kinetic energy
is 90% to its initial potential energy, as its initial kinetic is zero,i.e.,
K.E. = 
K.E. = 9000 J
Answer:
a)
, b) 
Explanation:
a) The Hooke's law states that spring force is directly proportional to change in length. That is to say:

In this case, the force is equal to the weight of the object:



The spring constant is:



b) The length of the spring is:




Answer:
1000 kgm²/s, 400 J
1000 kgm²/s, 1000 J
600 J
Explanation:
m = Mass of astronauts = 100 kg
d = Diameter
r = Radius = 
v = Velocity of astronauts = 2 m/s
Angular momentum of the system is given by

The angular momentum of the system is 1000 kgm²/s
Rotational energy is given by

The rotational energy of the system is 400 J
There no external toque present so the initial and final angular momentum will be equal to the initial angular momentum 1000 kgm²/s

Energy

The new energy will be 1000 J
Work done will be the change in the kinetic energy

The work done is 600 J
Momentum is a product mass and velocity. If a certain object posses a kinetic energy, then it should have a momentum since it is moving which has a velocity. However, if the object is at rest and only has potential energy, then it would not have momentum. So, for the first question the answer would be yes, an object can have energy without having any momentum. For the second question, every object whether it is moving or at rest, possess some energy, potential for an object at rest and kinetic for an object that is moving. Thus, the answer would be no, an object having momentum would always have energy.
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