First, let's find the angle of inclination using the tangent function.
sin θ = opposite/hypotenuse = 1 m/2 m
θ = 30°
Assuming the ramp is frictionless, the force balance is:
F = mgsinθ = ma
Cancelling out m,
a = gsinθ = (9.81 m/s²)(sin 30°) = 4.905 m/s²
Using the equation for rectilinear motion at constant acceleration,
x = v₀t + 0.5at²
2 m = (6 m/s)(t) + 0.5(4.905 m/s²)(t²)
Solving for tm
t = 0.297 seconds
Using the equation for acceleration:
a = (v - v₀)/t
4.905 m/s² = (v - 6 m/s)/0.297 s
Solving for v,
v = 7.46 m/s
