Answer:
I should be active for 15 hours to meet the physical activity requirement.
Explanation:
Since time dilates in moving objects, we use the formula t = t₀/√(1 - β²) where t = time in space vehicle, t₀ = time on earth = 9 hours and β = v/c where v = speed of space vehicle = 0.8c.
So, t = t₀/√(1 - β²)
t = 9/√(1 - (v/c)²)
= 9/√(1 - (0.8c/c)²)
= 9/√(1 - (0.8)²)
= 9/√(1 - (0.64)
= 9/√0.36
= 9/0.6
= 15 hr
So, according to a timer on the space vehicle, I should be active for 15 hours to meet the physical activity requirement.
Explanation:
Below is an attachment containing the solution.
The centripetal acceleration = 236.63 m/s²
The force = 17.98 N
<h3>Further explanation</h3>
Given
mass = 76 g = 0.076 kg
r = 1.5 m
f = 2 rps = 2 rotation per second
Required
The centripetal acceleration
The Force tension
Solution
Centripetal force is a force acting on objects that move in a circle in the direction toward the center of the circle

F = centripetal force, N
m = mass, Kg
v = linear velocity, m / s
r = radius, m
The speed that is in the direction of the circle is called linear velocity
Can be formulated:

r = circle radius
f = rotation per second (RPS)
The linear velocity : 2 x 3.14 x 1.5 x 2 =18.84 m/s
The centripetal acceleration : ac = v²/R = 236.63 m/s²
The force : F = m x ac = 0.076 x 236.63 = 17.98 N