How Fast Was the Bullet That Lodged in the Wooden Block?

[creynaud]

Homework Statement

A 2.0-kg block of wood rests on a tabletop. A 7.0-g bullet is shot straight up through a hole in the table beneath the block. The bullet lodges in the block, and the block flies 25 cm above the tabletop. How fast was the bullet going initially?

Homework Equations

initial m_bullet(initial v_bullet)+initial m_wood(initial v_wood)=(m_bullet+m_wood)Final v

The Attempt at a Solution

I know I am looking for the initial velocity of the bullet but how do I get the final velocity of the block of wood once it was hit by the bullet?

 

[Orodruin]

Look at the information you have. Is there some piece of information that might allow you to get the final velocity?

 

[creynaud]

the 25cm, I am just not sure how I could use it

 

[haruspex]

the 25cm, I am just not sure how I could use it

How fast would you need to throw a stone up for it to reach a height of 25cm? What equations do you know relating to constant acceleration, time, distance traveled etc?

 

[creynaud]

s=vi(t)+1/2(a)(t)^2
what would i put for time though?

 

[Orodruin]

What is the velocity at the height where it turns around?

Edit: You can also apply energy conservation, which will be less cumbersome.

 

[haruspex]

s=vi(t)+1/2(a)(t)^2
what would i put for time though?

There are five SUVAT equations. Each involves four of the variables: distance, initial speed, final speed, time, acceleration. As you note, you do not know what time to use, and you don't need to find it. So use the one equation that does not involve time. Also see Orodruin's reply.