The launching mechanism of a toy gun consists of a spring with an unknown spring constant, $k$. When the spring is compressed $0.120\,\text{m}$ vertically, a $35.0\,\text{g}$ projectile is able to be fired to a maximum height of $25\,\text{m}$ above the position of the projectile when the spring is compressed. Assume that the barrel of the gun is frictionless.

Question

The launching mechanism of a toy gun consists of a spring with an unknown spring constant, $k$. When the spring is compressed $0.120\,\text{m}$ vertically, a $35.0\,\text{g}$ projectile is able to be fired to a maximum height of $25\,\text{m}$ above the position of the projectile when the spring is compressed. Assume that the barrel of the gun is frictionless.(a) Where will you set $y = 0$? Explain your reasoning.
, (b) Determine the spring constant of the spring.
, (c) Determine the speed that the projectile is traveling the moment it leaves the spring.
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Jason · Accepted Answer

Where the spring is fully compressed
$k = \frac{17.15}{0.0144} \approx 1191.67 \, \text{N/m}$
$v = \sqrt{489.67} \approx 22.12 \, \text{m/s}$

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