A two-stage rocket accelerates from rest at +3.57 m/s/s for 6.82 seconds. It then

accelerates at +2.98 m/s/s for another 5.90 seconds. After the second stage, it enters

into a state of free fall. Determine:

a. the maximum speed

b. the maximum altitude

c. the height of the rocket after 20.0 seconds

d. the total time the rocket is in the air (assuming it is launched from the ground)

a) 750 rev/min

b) 450 rev/min

c) clockwise direction

Explanation:

We are given;

Rotational inertia of first disk;I_1 = 3.3 kg.m²

Angular velocity of first disk;ω_1 = 450 rev/min

Rotational Inertia of second disk;I_2 = 6.6 kg.m²

Angular velocity of second disk;ω_2 = 900 rev/min

Total rotational inertia;I_tot = 3.3 + 6.6 = 9.9 kg.m²

Since they couple together, we have;

I_tot × ω = (I_1 × ω_1) + (I_2 × ω_2)

Plugging in values, we have;

9.9ω = (3.3 × 450) + (6.6 × 900)

9.9ω = 7425

ω = 7425/9.9

ω = 750 rev/min

b) now, we are told the second disk is spinning clockwise, thus we have;

I_tot × ω = (I_1 × ω_1) - (I_2 × ω_2)

9.9ω = (3.3 × 450) - (6.6 × 900)

9.9ω = -4455

ω = -4455/9.9

ω = - 450 rev/min

The minus sign indicates a clockwise direction.