Gravity penetration

Classical Mechanics Level 3

A bullet fired into a fixed target losses half of its velocity after penetrating 3 cm into wood.

How much further will it penetrate before coming to rest?

DETAILS AND ASSUMPTIONS:-

1) Provide your answer in meters

The answer is 0.01.

1 solution

Caleb Townsend
Mar 14, 2015

Assuming constant acceleration, $\Delta x = (\frac{v_i + v_f}{2})t$ Also assuming constant acceleration, the time it takes to lose half speed is the same as the time to go from half speed to rest. Let $v$ be the bullet's initial speed, $\Delta x_1 = .03$ be the displacement from full speed to half, and $\Delta x_2$ be the displacement from half speed to rest. Then $\Delta x_1 = \frac{v + .5v}{2}t \\ \Delta x_2 = \frac{.5v + 0}{2}t \\ \frac{\Delta x_2}{\Delta x_1} = \frac{.25vt}{.75vt} = \frac{1}{3} \\ \Delta x_2 = \frac{.03\text{ m}}{3} = \boxed{.01\text{ m}}$

It can also be done in another way, can you try to post the other solution too.

HINT: Use the laws of motion.

Sravanth C. - 6 years, 3 months ago

I presume that you're saying to use $S_2=S_1\frac{(n-1)^2}{2n-1}$ Where n=2 , right?

Muhammad Arifur Rahman - 6 years, 3 months ago

Not exactly Arifur Rahman , I wanted him to use the LAWS OF MOTION

Sravanth C. - 6 years, 2 months ago

@Sravanth C. – From laws of motion you come up with that Equation I wrote.

That's why I said that I can do these Latex formatting to prove the equation.

Because its $V^2=U^2+2aS$ which all you need!

Muhammad Arifur Rahman - 6 years, 2 months ago

But Townsend's solution shows you a different way. Isn't it cool!

So you can post how I wrote the above using laws of motion .

Or, I can do those $\LaTeX$ jobs for you!

Muhammad Arifur Rahman - 6 years, 3 months ago

Sravanth likes the solution he did.

Can't you do him a favor!

Muhammad Arifur Rahman - 6 years, 3 months ago

Gravity penetration

The answer is 0.01.

1 solution

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