What is the initial speed of a bullet shot into a block on a frictionless table?

[oadeyemi]

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)

 

[satchmo05]

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

 

[oadeyemi]

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?

 

[satchmo05]

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

 

[oadeyemi]

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]

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.

 

[oadeyemi]

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.

Elaborate please

 

[Borek]

Once the bodies (m+M) left the table they behave just like something thrown norizontally - they maintain horizontal speed, but they start to fall down, till they hit the ground at distance d from the table border.