Answer:
2.55 m
Explanation:
The energy of the block is conserved. The block's initial kinetic energy (KE) is converted to gravitational potential energy (PE). The kinetic energy is equal to half the mass (m) times the square of the speed (v), and the potential energy is equal to the weight (mg) times the height (h). Once we find the height, we can use trigonometry to find the distance along the plane.
KE = PE
½ mv² = mgh
½ v² = gh
h = ½ v² / g
h = ½ (5.00 m/s)² / (9.8 m/s²)
h = 1.28 m
Using trigonometry:
sin θ = h / L
sin 30° = 1.28 m / L
L = 2.55 m
