# Bullet shot into a block

## Homework Statement

A bullet of mass m is fired into a block of mass M initially at rest on a frictionless table of height h. The bullet remains m in the block, and after impact the block lands a distance d from the bottom of the table. Determine the initial speed of the bullet.

## Homework Equations

I used (m +M)gh for the potential energy and set that equal to the kinetic energy ½(m + M)v₂² and found that v₂ = √(2gh).

And since it was a completely inelastic collision (right?) I used mv₁ = (m + M)v₂ → v₁ = (m + M)v₂ * 1/m

Is this right?

## The Attempt at a Solution

initial velocity = √(2gh)*((m + M)/m)

Last edited:

Do you have an attempt at the problem? If not, tell me your thought process for the problem.

Do you have an attempt at the problem? If not, tell me your thought process for the problem.

I used (m +M)gh for the potential energy and set that equal to the kinetic energy ½(m + M)v₂² and found that v₂ = √(2gh).

And since it was a completely inelastic collision (right?) I used mv₁ = (m + M)v₂ → v₁ = (m + M)v₂ * 1/m

Is this right?

I used mv₁ = (m + M)v₂ → v₁ = (m + M)v₂ * 1/m

Something about this chunk doesn't seem right to me for some reason. Everything else is correct, from my understanding. Is this a formula you received from your text, or is this something that you derived yourself?

Check out the Wiki article, I think I see where you're going with this, but I see a slight error in your formula: http://en.wikipedia.org/wiki/Inelastic_collision

Something about this chunk doesn't seem right to me for some reason. Everything else is correct, from my understanding. Is this a formula you received from your text, or is this something that you derived yourself?

Check out the Wiki article, I think I see where you're going with this, but I see a slight error in your formula: http://en.wikipedia.org/wiki/Inelastic_collision

It's from my textbook

Borek
Mentor
I think the formula here is OK, wiki describes different situation (initial velocity of M not being zero) and uses different symbols, hence the confusion.

Problems are with the other part - v2 that you calculated from the energy conservation is a vertical component of the speed when block with a bullet hits the ground. That's not initial HORIZONTAL speed of the body.

I think the formula here is OK, wiki describes different situation (initial velocity of M not being zero) and uses different symbols, hence the confusion.

Problems are with the other part - v2 that you calculated from the energy conservation is a vertical component of the speed when block with a bullet hits the ground. That's not initial HORIZONTAL speed of the body.