<span>Ans : Initial E = KE = ½mv² = ½ * 1.2kg * (2.2m/s)² = 2.9 J
max spring compression where both velocities are the same: conserve momentum:
1.2kg * 2.2m/s = (1.2 + 3.2)kg * v → v = 0.6 m/s
which means the combined KE = ½ * (1.2 + 3.2)kg * (0.6m/s)² = 0.79 J
The remaining energy went into the spring:
U = (2.9 - 0.79) J = 2.1 J = ½kx² = ½ * 554N/m * x²
x = 0.0076 m ↠(a)</span>
6050 J is the kinetic energy at D
<u>Explanation:</u>
In physics, the object's kinetic energy (K.E) defined as the energy it possesses during movement. It can be defined as the required work to accelerate a certain body weight in order to rest at a certain speed. When the body receives this energy as it speeds up (accelerates), it retains this energy unless speed varies. The equation is given as,

Where,
m - mass of an object
v - velocity of the object
Here,
Given data:
m = 100 kg
v = 11 m/s
By substituting the given values in the above equation, we get

Here it is an application of Newton's III law
as we know by Newton's III law that every action has equal and opposite reaction
So here as we know that two boys jumps off the boat with different forces
from front side of the boat the boy jumps off with force 45 N which means as per Newton's III law if boy has a force of 45 N in forward direction then he must apply a reaction force on the boat in reverse direction of same magnitude
So boat must have an opposite force on front end with magnitude 45 N
Now similar way we can say
from back side of the boat the boy jumps off with force 60 N which means as per Newton's III law if boy has a force of 60 N in backward direction then he must apply a reaction force on the boat in reverse direction of same magnitude
So boat must have an opposite force on front end with magnitude 60 N
So here net force due to both jump on the boat is given by



so boat will have net force F = 15 N in forward direction due to both jumps
The most exact answer is 78.4J also in this kind of options we can say answer "d"