Answer:
ma = 48.48kg
Explanation:
To find the mass of the astronaut, you first calculate the mass of the chair by using the information about the period of oscillation of the empty chair and the spring constant. You use the following formula:
(1)
mc: mass of the chair
k: spring constant = 600N/m
T: period of oscillation of the chair = 0.9s
You solve the equation (1) for mc, and then you replace the values of the other parameters:
(2)
Next, you calculate the mass of the chair and astronaut by using the information about the period of the chair when the astronaut is sitting on the chair:
T': period of chair when the astronaut is sitting = 2.0s
M: mass of the astronaut plus mass of the chair = ?
(3)
Finally, the mass of the astronaut is the difference between M and mc (results from (2) and (3)) :

The mass of the astronaut is 48.48 kg
Answer:
Explanation:
Given that:
the initial angular velocity 
angular acceleration
= 4.44 rad/s²
Using the formula:

Making t the subject of the formula:

where;

∴

t = 0.345 s
b)
Using the formula:

here;
= angular displacement
∴



Recall that:
2π rad = 1 revolution
Then;
0.264 rad = (x) revolution

x = 0.042 revolutions
c)
Here; force = 270 N
radius = 1.20 m
The torque = F * r

However;
From the moment of inertia;

given that;
I = 84.4 kg.m²

For re-tardation; 
Using the equation



t = 0.398s
The required time it takes= 0.398s
Faster than. Hope this helps!!!