(Solved): A student performs a ballistic pendulum experiment using an apparatus similar to that shown in the ...

A student performs a ballistic pendulum experiment using an apparatus similar to that shown in the figure. Initially the bullet is fired at the block while the block is at rest (at its lowest swing point). After the bullet hits the block, the block rises to its highest position, see dashed block in the figure, and continues swinging back and forth. The following data is obtained: the maximum height the pendulum rises is $$2\mathrm{cm}$$, at the maximum height the pendulum subtends an angle of $$29.9^{?}$$, the mass of the bullet is $$66\mathrm{g}$$, and the mass of the pendulum bob is $$792\mathrm{g}$$. Determine the initial speed of the projectile. The acceleration due to gravity is $$9.8\mathrm{m}/{\mathrm{s}}^2$$. Answer in units of $$\mathrm{m}/\mathrm{s}$$.