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
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At the current rate of uranium consumption with conventional reactors, the world supply of viable uranium, which is the most common nuclear fuel, will last for 80 years. Scaling consumption up to 15 TW, the viable uranium supply will last for less than 5 years
