Answer:
The right solution is "24.39 per sec".
Explanation:
According to the question,
⇒ 

The time will be:
⇒ 



hence,
⇒ 

(a) The spring stiffness constant of the spring is 18,392 N/m.
(b) The time the car was in contact with the spring before it bounces off in the opposite direction is 0.23 s.
<h3>Kinetic energy of the car</h3>
The kinetic energy of the car is calculated as follows;
K.E = ¹/₂mv²
K.E = ¹/₂ x 950 x 22²
K.E = 229,900 J
<h3>Stiffness constant of the spring</h3>
The stiffness constant of the spring is calculated as follows;
K.E = U = ¹/₂kx²
k = 2U/x²
k = (2 x 229,900)/(5)²
k = 18,392 N/m
<h3>Force exerted on the spring</h3>
F = kx
F = 18,392 x 5
F = 91,960 N
<h3>Time of impact</h3>
F = mv/t
t = mv/F
t = (950 x 22)/(91960)
t = 0.23 s
Learn more about spring constant here: brainly.com/question/1968517
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Answer:
The angular velocity is 
Explanation:
From the question we are told that
The mass of each astronauts is 
The initial distance between the two astronauts 
Generally the radius is mathematically represented as 
The initial angular velocity is 
The distance between the two astronauts after the rope is pulled is 
Generally the radius is mathematically represented as 
Generally from the law of angular momentum conservation we have that

Here
is the initial moment of inertia of the first astronauts which is equal to
the initial moment of inertia of the second astronauts So

Also
is the initial angular velocity of the first astronauts which is equal to
the initial angular velocity of the second astronauts So

Here
is the final moment of inertia of the first astronauts which is equal to
the final moment of inertia of the second astronauts So

Also
is the final angular velocity of the first astronauts which is equal to
the final angular velocity of the second astronauts So

So

=> 
=> 
=> 
=> 