Answer
0.18m
Work Step by Step
The dart is thrown horizontally, meaning that it has no velocity in the y component, only in the x (horizontal component). However, it has acceleration in the y direction due to gravity at a = -9.81 $m/s^2$
We can use the equation:
$ y = y0 + v_{0y}t + (1/2)a_{y}t^2 $
We can rewrite this as
$\Delta y = v_{0y}t + (1/2)a_{y}t^2 $
we know that $v_{0y}$ = 0 as discussed above and a = -9.81$m/s^2$ and the dart takes 0.19 seconds to hit the board (t = 0.1) so
$\Delta y = (1/2)(-9.81)(0.19)^2 = 0.18m $
This is how far the dart will drop from the horizontal while it is in flight, and therefore, it is the length of PQ
