Answer
210N
Work Step by Step
The toothpick was moving at 220m/s and its penetration depth was 15mm or 0.015m. This means that in 0.015m the velocity went from 200m/s to 0m/s. Using the equation:
$v^@ = v_{0}^2 + 2a\Delta x $ we can solve for acceleration where v0 = 200m/s and $\Delta x$ = 0.015m
We find this to be a = $1613333 m/s^2$
Since F = ma and the mass was 0.13g or 0.00013kg then F = 210N
