Your equations are correct (although as I said in my other comment 9.81 is the global average but gravity varies by ~0.1 so that’s too many significant figures), but their issue doesn’t have to do with using sloped distance, by which I assume you mean the length of the slope (they don’t as far as I can tell). It says the height change is 2 meters, and they use 2 meters as the distance since that’s the component of the displacement parallel to gravity. The problem is that they didn’t convert mass to weight.
work = average force • displacement = |average force| * |displacement| * cos(angle between them)
= component of average force parallel to displacement * |displacement|
= component of displacement parallel to force * |average force|
weight = force due to gravity = mass * acceleration due to gravity ≈ 5 kg * 9.8 m/s² = 49 N
work = component of displacement parallel to average force * |average force|
= 2 m * weight
≈ 98 Nm
Your equations are correct (although as I said in my other comment 9.81 is the global average but gravity varies by ~0.1 so that’s too many significant figures), but their issue doesn’t have to do with using sloped distance, by which I assume you mean the length of the slope (they don’t as far as I can tell). It says the height change is 2 meters, and they use 2 meters as the distance since that’s the component of the displacement parallel to gravity. The problem is that they didn’t convert mass to weight.
work = average force • displacement = |average force| * |displacement| * cos(angle between them) = component of average force parallel to displacement * |displacement| = component of displacement parallel to force * |average force| weight = force due to gravity = mass * acceleration due to gravity ≈ 5 kg * 9.8 m/s² = 49 N work = component of displacement parallel to average force * |average force| = 2 m * weight ≈ 98 NmOP specifically asked about the sloped distance:
Ah, my mistake.