Answer
See the detailed answer.
Work Step by Step
a) A 0.5-kg block was attached to a 400-N/m-spring on an inclined frictionless surface. The spring has initially compressed a distance of 10 cm, then released pushing the block up the incline until it is no longer touching it. If you know that the block traveled a distance of 10 cm up the incline from its initial position and that the incline is making an angle of 30$^\circ$ with the horizontal line, what is its final speed $v_f$?
b) See the figure below.
c) Solving for $v_f$;
$$v_f=\sqrt{\dfrac{(0.5\times 9.8\times -0.1\times \sin30^\circ)+(\frac{1}{2}\times 400\times 0.1^2)}{\frac{1}{2}\times 0.5}}$$
$$v_f=\color{red}{\bf 2.65}\;\rm m/s$$
