Answer:
(A) the angular acceleration of the blades is 13.33 m/s.
Explanation:
Given;
moment of inertia of a blade, I = 0.2 kgm²
net torque exerted on fan blades, ∑τ = 8Nm
Torque is given as product of moment of inertia and angular acceleration;
τ = Iα
where;
α is the angular acceleration
Since there are three blades of the ceiling fan, the net torque is given as;
∑τ = (3I)α
∑τ = 3Iα
α = ∑τ / 3I
α = (8) / (3 x 0.2)
α = 13.33 m/s
Therefore, the angular acceleration of the blades is 13.33 m/s.
Answer:
The thrown rock strike 2.42 seconds earlier.
Explanation:
This is an uniformly accelerated motion problem, so in order to find the arrival time we will use the following formula:

So now we have an equation and unkown value.
for the thrown rock

for the dropped rock

solving both equation with the quadratic formula:

we have:
the thrown rock arrives on t=5.4 sec
the dropped rock arrives on t=7.82 sec
so the thrown rock arrives 2.42 seconds earlier (7.82-5.4=2.42)