a pneumatic nail gun with muzzle speed of 37m/s fires a 5.0cm nail directly into a hard wood that stops the nail just when it is full embedded in the wood. Assuming the nail's deceleration to be constant, what is its magnitude?

Average velocity during penetration

= 37/2 = 18.5 m/s
Penetration time = 0.05m/18.5 m/s
= 2.70*10^-3 s
Deceleration rate magnitude
= 37/2.7*10^-3 = 13,690 m/s^2

That's a lot of g's (about 1400)

To find the magnitude of the nail's deceleration, we can use the equations of motion. Let's break down the problem to find all the relevant information.

Given:
- Initial speed (u) = 37 m/s
- Distance traveled (s) = 5.0 cm = 0.05 m (since the nail is fully embedded in the wood, it has traveled the full distance of 5.0 cm)
- Final speed (v) = 0 m/s (the nail comes to rest)

We need to find the magnitude of deceleration (a).

We can use the equation of motion:

v^2 = u^2 + 2as

Rearranging the equation, we have:

a = (v^2 - u^2) / (2s)

Now, substitute the given values into the equation:

a = (0^2 - 37^2) / (2 * 0.05)

Simplifying the equation further:

a = (-1369) / 0.1

a = -13690 m/s^2

The magnitude of the nail's deceleration is 13690 m/s^2. Note that the negative sign indicates deceleration, as the speed is decreasing.