We can start by breaking down the 16.0 N force into its components parallel and perpendicular to the slope.
The force parallel to the slope is given by F = mgsin(20°), where m is the mass of the block and g is the acceleration due to gravity. Plugging in the values, we get:
F = (3.0 kg)(9.81 m/s^2)sin(20°) = 9.81 N
This is the net force acting on the block parallel to the slope. Using Newton's second law, we can find the acceleration of the block as:
a = F/m = 9.81 N / 3.0 kg = 3.27 m/s^2
Since the slope is frictionless, there is no opposing force, and the entire force parallel to the slope goes towards accelerating the block.
Now, to find the distance traveled by the block in 2.0 seconds, we can use the kinematic equation:
x = (1/2)at^2
where x is the distance traveled, a is the acceleration, and t is the time. Plugging in the values, we get:
x = (1/2)(3.27 m/s^2)(2.0 s)^2 = 6.54 meters
Therefore, the block travels 6.54 meters up the slope in 2.0 seconds
Hope this helped!