Bullet penetrating a block problem

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A rifle fires a 10g bullet at 400 m/s, which penetrates a block of wood to a depth of 12 cm. The acceleration of the bullet while in the block is calculated using the equation Vf² = Vi² + 2aX, resulting in a value of -6.7 x 10^5. However, when attempting to find the time it takes for the bullet to come to rest using X = Vit + 1/2 at², the user encounters a function with no real roots. The discussion highlights the need to double-check calculations and suggests that posting work may help identify errors. Accurate application of kinematic equations is essential for solving the problem correctly.
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Homework Statement


a rifle with a barell length of 60 cm fires a 10g bullet with a horizontal speed of 400 m/s. the bullet strikes a block of wood and penetrates to a depth of 12 cm. how long does it take the bullet to come to rest( from when it penetrates the block to when it stops)?



Homework Equations


kinematic equations


The Attempt at a Solution


we can figure out the acceleration of the bullet while its in the block with
Vf2= Vi2 + 2aX which gives -6.7*105

but now when i try to use X= Vit + 1/2 at2 to figure out time it give me a function with no real roots
what am i doing wrong here?
 
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Any other kinematic equations you may have overlooked?
 
dont worry i haven't forgotten about the other equations :)
i was just wondering why this one didnt work
 
I get a real, double root when I solve it using your method, so you must be making an error somewhere in your work...If you actually post your work, I can point it out to you. :wink:
 
oops guess i better double check that
thanks for the help :biggrin:
 

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