A 6.00-kg block starts from rest and slides down a frictionless incline. When the block has slid a distance 2.00 m, its speed is 3.00 m/s. At what angle above horizontal is the inclined plane tilted?

The angle above horizontal is 13.3°.

Explanation:

The angle can be calculated with Newton's third law:

Where:

ΣF: is the forces acting on the object

m: is the mass of the object = 6.00 kg

a: is the acceleration of the object

The only force acting on the object is the weight since there is no friction, so:                  

  (1)

Where:

θ: is the angle

g: is the acceleration due to gravity = 9.81 m/s²

We can find the acceleration from the following kinematic equation:

Where:

: is the final speed = 3.00 m/s

: is the initial speed = 0 (the block starts from rest)

d: is the distance traveled = 2.00 m

The acceleration is:

Finally, the angle is (equation 1):

Therefore, the angle above horizontal is 13.3°.

I hope it helps you!