Answer :
Answer:
Horizontal launch
[tex]\vec v = 2.739\cdot i \,\left[\frac{m}{s} \right][/tex]
Vertical launch
[tex]\vec v = 2.739\cdot j \,\left[\frac{m}{s} \right][/tex]
Explanation:
The launch speed is calculated by means of the Principle of Energy Conservation:
[tex]U_{k} = K[/tex]
[tex]\frac{1}{2}\cdot k \cdot x^{2} = \frac{1}{2}\cdot m \cdot v^{2}[/tex]
[tex]v = x \cdot \sqrt{\frac{k}{m} }[/tex]
[tex]v = (0.15\,m)\cdot \sqrt{\frac{100\,\frac{N}{m} }{0.3\,kg} }[/tex]
[tex]v \approx 2.739\,\frac{m}{s}[/tex]
The velocities for each scenario are presented herein:
Horizontal launch
[tex]\vec v = 2.739\cdot i \,\left[\frac{m}{s} \right][/tex]
Vertical launch
[tex]\vec v = 2.739\cdot j \,\left[\frac{m}{s} \right][/tex]