Answer
4.00 m
Work Step by Step
Looking at the incline as a right triangle, we see that the change in height the block undergoes is Δh = d sin θ, where d is the distance traveled along the incline.
From Problem 31b, we know that $ΔU_{g}$ = 39.2 J. So to find d, we can plug in these values in the equation for $ΔU_{g}$ and solve for d:
$ΔU_{g}= mgΔh$
$ΔU_{g} = mgdsinθ$
$d = \frac{ΔU_{g}}{mg sin θ}$
$d = \frac{39.2 J}{(2.00 kg)(9.8 m/s²) sin 30.0^{\circ}}$
$d$ = 4.00 m
