What Is the Bullet's Exit Speed After Passing Through a Block?

[Memetics]

Homework Statement

A bullet with a mass of 4.0 g and a speed of 661 m/s is fired at a block of wood with a mass of 0.075 kg. The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 25 m/s. What is the speed of the bullet when it exits the block?

m1 = 4g -> 0.004 kg
v1b = 661 m/s
v1a = ?
m2 = 0.075 kg
v2b = 0 m/s
v2a = 25 m/s

Homework Equations

m1v1b + m2v2b = m1v1a + m2v2a

The Attempt at a Solution

m1v1b + m2v2b = m1v1a + m2v2a
(.004)(661) = (.004)(v1a) + (.075)(25)
2.664 = (.004)(v1a) + 1.875
.789 = .004v1a
197.25 m/s = v1a

I've double checked this and gotten the same answer twice, but we have to use WebAssign, and the error it gives is "Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error." which I don't understand? I don't see what's been done wrong, and there's other parts of the problem I can't continue to until this is done. Any help would greatly be appreciated!

 

[anathema]

Thank you for your question. After reviewing your attempt at a solution, it seems like you have made a small error in your calculation. The correct value for v1a should be 197.25 m/s, not 1972.5 m/s. This is likely due to a rounding error in your intermediate calculations. To minimize roundoff error, it is important to carry out all intermediate results to at least four-digit accuracy. In this case, you should use 2.664 instead of 2.66 and 1.875 instead of 1.88 in your calculation.

I hope this helps and please let me know if you have any further questions.



Scientist

 

[tomcue]

I would first like to commend you for showing your work and attempting to solve the problem on your own. Your solution is correct and your approach is sound. However, the error message from WebAssign may be due to the fact that you have rounded off your intermediate calculations to only three significant figures. To minimize roundoff error, it is recommended to carry out all intermediate results to at least four-digit accuracy. This means keeping track of all digits in your calculations, not just the final answer. When you do this, you should get a final answer of 197.3 m/s, which is within the 10% margin of error given by WebAssign. I hope this helps clarify the issue and good luck with the rest of your problem!