Final answer:
To find the block's speed after traveling 2.0 m up an inclined plane, we can use the work-energy principle. The work done on the block is equal to its change in kinetic energy. Using the given values, the speed of the block after traveling 2.0 m is 10.95 m/s.
Step-by-step explanation:
To find the block's speed after traveling 2.0 m up an inclined plane, we can use the work-energy principle. The work done on the block is equal to its change in kinetic energy. The work done is given by the force times the distance, where the force is the component of the block's weight parallel to the incline and the distance is the distance the block travels along the incline.
Using the equation for work, we have:
Work = force · distance = m·g·d·sin(θ)
Where m is the mass of the block, g is the acceleration due to gravity, d is the distance traveled along the incline, and θ is the angle of the incline.
Next, we set the work done equal to the change in kinetic energy:
Work = ½m·v² - ½m·u²
Where v is the final velocity of the block and u is the initial velocity of the block. Rearranging the equation, we get:
v² = u² + 2g·d·sin(θ)
Plugging in the given values, we have:
v² = (9.0 m/s)² + 2(9.8 m/s²)(2.0 m)sin(38°)
v² = 81 m²/s² + 38.8 m²/s²
v² = 119.8 m²/s²
Taking the square root of both sides, we find the speed of the block after it has traveled 2.0 m:
v = 10.95 m/s