Momentum, Impulse, and Collisions: Wooden Block Shot with a bullet

[ahorowitz1]

1.So the problem given is the following, "A small wooden block with mass 0.775 kg is suspended from the lower end of a light cord that is 1.58m long. The block is initially at rest. A bullet with mass 0.0134 kg is fired at the block with a horizontal velocity[UP][/UP] v₀. The bullet strikes the block and becomes embedded in it. After the collision the combined object swings on the end of the cord. When the block has risen a vertical height of 0.700 m , the tension in the cord is 4.92N."


2. Right now the I can figure out a few equations from this. I know that because the bullet becomes embedded in the wooden block, it can be considered a perfect inelastic collision. Thus m1v1 + m2v2 = (m1 + m2)vf. For this problem, I'm going to call the bullet m1 and the wooden block m2. Thus, I know that from this I can solve for the final velocity of the two embedded object. Also, I figure that because the block is on a string, and it is moving, that centripetal force/ acceleration must come into play. Therefore, should I use the equation F_C=ma_c=T - mg?

3. v_f=(0.0134kg * v₀+ 0.775 kg * 0 m/s) / (0.0134 kg + 0.775 kg) = 0.016996 v₀. However, I'm confused as to how to progress from here? I know that the tension when the object (combined) has reached 0.700 m is equal to 4.92 N, but I'm having difficult picturing this. Does this tension value represent the tension when the 1.58 m string is facing right, forming a triangle of sorts where 1.58 is the hypotenuse and the y-component is 0.88m? Please let me know how to progress from here, or at least if you know how I should be visualizing this that would be so helpful! Thanks!

EDIT: The question is what is the initial speed V₀ of the bullet?

 

[rude man]

What is the question?

 

[Simon Bridge]

Welcome to PF;
rude man is correct - you have not provided a complete problem statement, just a bunch of facts. I'm guessing you need to find $v_0$.

You did ask a question of sorts:

Does this tension value represent the tension when the 1.58 m string is facing right, forming a triangle of sorts where 1.58 is the hypotenuse and the y-component is 0.88m? Please let me know how to progress from here, or at least if you know how I should be visualizing this that would be so helpful! Thanks!

The tension points along the string and is the same as how you'd normally view the tension.

You should be able to sketch the final position - you know the length of the cord and you know the vertical height is has swung to.
If you draw a free body diagram, you should be able to figure out the centripetal force and thus the final speed.

Take care using conservation of momentum when there is an unbalanced force.