Answer :
There are 4 questions here that need to be solved.
a. The velocity of the astronaut & book system after the collision (using conservation of momentum) is 0.19 m/s
b. The initial kinetic energy of the system is 24J
c. The final kinetic energy of the system is 1.14J
d. The impulse exerted by the book on the astronaut is 11.43 kg.m/s
What is kinetic energy?
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during acceleration, the body maintains this kinetic energy unless its speed changes.
Now, let's answer the question.
a.
m1 book = 3kg
m2 astronaut = 60kg
vi1 = 4m/s
vi2 = 0m/s
Vf = final speed after collision
Now, let calculate using conservation of momentum formula
ρi = ρf
m1 * vi1 + m2 * v2 = (m1 + m2) * vf
3 * 4 + 60 * 0 = (3 + 60) * vf
12 = 63vf
vf = 0.19 m/s (rounded)
So, the velocity of the astronaut-book system after the collision is 0.19 m/s.
b. Initial kinetic energy will be calculated using kinetic energy formula
KEi = 1/2 * m1 * Vi1^2
= 1/2 * 3 * 4^2
= 24J
So, the initial kinetic energy of the system is 24J
c. Final kinetic energy will be calculated as follows
KEf = 1/2 * (m1 + m2) * vf^2
= 1/2 * (3 + 60) * 0.19^2
= 1.137J
So, the final kinetic energy of the system is 1.137J
d. To calculate the impulse, it is basically the change in momentum of the book, calculated as follows
I (impulse) = m1 * (Vi1 - Vf)
= 3 * (4-0.19)
= 11.43 Kg.m/s
Therefore, the impulse exerted by the book on the astronaut is 11.43 Kg.m/s
Learn more about kinetic energy https://brainly.com/question/26472013
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