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A bullet moving with a velocity of 200cm/s penetrates a wooden block and comes to rest after traversing 4cm inside it . What velocity is needed for travelling distance of 9cm in same block. My though for this question:

Q1 By 200m/s , does it mean the speed just before it touched the block and during that time it may have either had some acc or not.

Online answer: They solved it this way that they found acc of bullet with 200cm/s. Then they equated the same acc of 200cm/s with the acc formula for finding the new velocity. They got 300m/s.

My thought for this question. Why did the they take the same acc.You can just take any value of acc and find v in such a way that it pierces 9m though the block. I think I am confusing with 1st part. Bcuz acc will matter since we have F =ma. Please tell where am I going wrong. enter image description here

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  • $\begingroup$ Please tell where am I going wrong. Check-my-work questions are off-topic on this site. $\endgroup$
    – G. Smith
    Commented Nov 14, 2020 at 4:45

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First of all, Here we are assuming constant retardation in the velocity of the bullet when it penetrates through the block. It's because the block is assumed to be constant density through its volume (and homogeneous).

Now assuming that the block just provides constant retardation. We can compute How much distance the bullet penetrates through the block with the equation of motion $$v^2=u^2-2|a|s$$ We know that the final velocity should be zero ie. $v=0$.

I think I am confusing with 1st part. Bcoz acc will matter since we have $F =ma$.

Note that as I said we are assuming constant retardation so that a constant force (which becomes zero as the bullet gets stop) against the motion of the bullet.

Edit: Note that retardation can be treated as property of block. So once If we shoot the bullet to see what's it's retardation is by calculating penetaration length. Retardation will same for the other cases.

In the present case, When we have shoot the bullet with $2$ m/sec. It penetarate through $4$ cm. Thus we can find the retardation that is as calculated turn out to be $50 m/sec^2$. Now, this retardation is fix for all other cases.

So next time when you need to calculate penetaration length, you can use this as retardation.

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  • $\begingroup$ It is really helpful.Why do we assume acc to be 0.9 then?. $\endgroup$
    – user277768
    Commented Nov 13, 2020 at 17:52
  • $\begingroup$ kidaichi please help me with this and Q1 $\endgroup$
    – user277768
    Commented Nov 13, 2020 at 17:53
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    $\begingroup$ I extended the answer. $\endgroup$
    – Himanshu
    Commented Nov 13, 2020 at 18:41
  • $\begingroup$ Why is retardation same for all cases ? $\endgroup$
    – user277768
    Commented Nov 13, 2020 at 18:46
  • $\begingroup$ As I have written, It's a property of a block. $\endgroup$
    – Himanshu
    Commented Nov 13, 2020 at 19:00