Frictionless ramp: The acceleration of a box sliding down a frictionless ramp inclined at 30 degrees can be determined using the equation for gravitational acceleration:
a = g * sin(θ)
where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the ramp (30 degrees).
a = 9.8 * sin(30) = 4.9 m/s^2
Ramp with friction: If the coefficient of friction between the box and ramp is 0.34, the acceleration can be determined using the equation:
a = g * sin(θ) - μ * g * cos(θ)
where μ is the coefficient of friction.
a = 9.8 * sin(30) - 0.34 * 9.8 * cos(30) = 2.86 m/s^2
So the acceleration of the box sliding down a frictionless ramp inclined at 30 degrees is 4.9 m/s^2, and the acceleration if the coefficient of friction is 0.34 is 2.86 m/s^2.