Question

We need to find the launch velocity of our new marble launcher. we know that it will launch a 25g marble to a distance of 73 cm, causing an impact noise of 44 decibels. the marble will then roll up to 6.2 meters befor stopping. with a launch height of 20 cm and a classroom temperature of 15.8 degrees celsius, we can calculate the launch velocity of the marble launcher to be

Answer 1

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 + $\frac{1}{2}$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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