# Problem on Dynamics . Help me to figure it out.

#### taiturab

A bullet can enter
50 cm in a wood
30 cm in a wall
100 cm in water .

If there is
1) a 10 cm wood at first
2) then 2 cm wall in the second
3) Layer of water at last .

Q.) How much distance the bullet will go in the water ?

#### topsquark

Forum Staff
A bullet can enter
50 cm in a wood

If there is
1) a 10 cm wood at first
These seem to contradict each other. Could you explain what you are doing in more detail?

-Dan

taiturab

#### studiot

This is a problem in simultaneous or coupled equations, that is not as bad as it seems.

So I will give you a start

Assume constant deceleration in all cases.

Let
v0 be the approach velocity of the bullet in all cases.
-a1 be the deceleration in wood
-a2 be the deceleration in the wall
-a3 be the deceleration in water

Then using $$\displaystyle {v^2} = {u^2} + 2as$$ and the information about the distances which each bring the bullet to a standstill

$$\displaystyle 0 = v_0^2 - 2{a_1}*50$$

$$\displaystyle 0 = v_0^2 - 2{a_2}*30$$

$$\displaystyle 0 = v_0^2 - 2{a_3}*100$$

or

$$\displaystyle 100{a_1} = 60{a_2} = 200{a_3}$$

Which reduces 4 unknowns to 2.

If we now let
S be the unknown distance in water to be found can you generate some more equations to solve this?

#### Cervesa

bullet’s initial kinetic energy - work done by medium = 0

for wood, $\dfrac{1}{2}mv^2 = F_a \cdot 0.5 \implies |F_a| = mv^2$

for wall, $\dfrac{1}{2}mv^2 = F_b \cdot 0.3 \implies |F_b| = \dfrac{5}{3}mv^2$

for water, $\dfrac{1}{2}mv^2 = F_c \cdot 1.0 \implies |F_c| = \dfrac{1}{2}mv^2$

$\dfrac{1}{2}mv^2 = |F_a| \cdot 0.1 + |F_b| \cdot 0.02 + |F_c| \cdot \Delta x$

solve for $\Delta x$

#### studiot

bullet’s initial kinetic energy - work done by medium = 0
You have the mass of the bullet to calculate this?

taiturab

#### Cervesa

You have the mass of the bullet to calculate this?
every term in the last equation has a factor of $mv^2$

#### taiturab

Thanks a lot . It'll be more easier for me if you further explain . How to calculate the s. I hope you will .

#### taiturab

Thanks a ton . i was suffering from this problem . It was really easy . Again Thanks a lot .