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 + $\frac{1}{2}$ g $t^{2}$

Let u = 0

0.2 = 0×t + $\frac{1}{2}$ × 9.8 × $t^{2}$

$t^{2}$ = $\frac{0.2}{4.9}$

$t^{2}$ = 0.04

t = 0.2s

Now, the launch velocity of the marble launcher can be calculated by:

Speed = Distance / Time

Speed = $\frac{0.73 + 6.3}{0.2}$

Speed = $\frac{6.93}{0.2}$

Speed = 34.65 m/s

Therefore, the launch velocity of the marble launcher is 34.65 m/s

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