The launch velocity of the marble launcher is 34.65 m/s
Given that the launch velocity of marble launcher, launches a 25g marble to a distance of 73 cm (0.73 m) and the marble roll up to 6.2 meters before stopping. The launch height is 20 cm (0.2 m).
The time for landing can be calculated by the second equation of motion formula:
h = ut +
g
Let u = 0
0.2 = 0×t +
× 9.8 × 
= 
= 0.04
t = 0.2s
Now, the launch velocity of the marble launcher can be calculated by:
Speed = Distance / Time
Speed = 
Speed = 
Speed = 34.65 m/s
Therefore, the launch velocity of the marble launcher is 34.65 m/s
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Answer:
The magnitude of the average angular acceleration of the disk is
.
Explanation:
Given that,
Angular velocity, 
The disk comes to rest, 
Time, t = 0.234 s
We need to find the magnitude of the average angular acceleration of the disk. It is given by change in angular velocity per unit time. So,

So, the magnitude of the average angular acceleration of the disk is
.
That will depend on the coefficient of friction between the sliding surfaces, and also on Zak's weight. We don't have any of that information.