Answer
$1.18$ meters
Work Step by Step
Ref to the attached figure....the Free Body Diagram. g = accl due to gravity.
Acceleration along the incline acting against the motion is $a = -g * sin \theta$
When it stops, the speed $v$ = 0. t = time to stop.
Using $v = v_{0} + at$, we get $t = - v_{0}/a$.
now $\Delta x$ = distance traveled by the block on the incline = $v_{0}t + \frac{1}{2}at^{2}$.
Replace $t = - v_{0}/a$.
we get $\Delta x$ = $v_{0} * (- v_{0}/a) + \frac{1}{2}a(- v_{0}/a)^{2}$ = $-\frac{1}{2} (v_{0}^{2}/a)$
= $\frac{-\frac{1}{2} * (3.5)^{2}} {(9.8) * sin 32^{\circ}}$
= $1.18$ meters
