Final answer:
To find the final velocity of the block, we can use the equations of motion. The acceleration of the block can be calculated using the angle of the incline and the acceleration due to gravity. The work done by gravity can be calculated using the mass of the block and the vertical distance traveled along the incline. The angle of the incline can be found using the formula tan(theta) = h/s.
Step-by-step explanation:
To find the final velocity (v) of the block, we can use the equations of motion. Since the block starts from rest, its initial velocity (u) is 0. The distance (s) traveled down the incline is 2.00 m and the time (t) taken is 1.5 s. Using the equation v = u + at, we can find the acceleration (a) of the block. Since the block is sliding down the incline, the acceleration is along the incline and can be given by a = g*sin(theta), where g is the acceleration due to gravity and theta is the angle of the incline.
Using g = 9.8 m/s² and the given angle of 30.0°, we can calculate the acceleration. Once we have the acceleration, we can use the equation s = ut + 0.5at² to find the final velocity of the block.
The work done by gravity (W) is given by W = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the vertical distance traveled by the block along the incline.
The angle of the incline can be found using the formula tan(theta) = h/s.