Final answer:
To solve this problem, we can use the principle of conservation of mechanical energy. The initial kinetic energy of the cylinder is equal to the final potential energy of the cylinder at its highest point on the incline. Using the given values of the angle of the incline and initial velocity, we can calculate that the solid cylinder travels approximately 12.7 meters up the incline.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of mechanical energy. The initial kinetic energy of the cylinder is equal to the final potential energy of the cylinder at its highest point on the incline. We can calculate the final height by equating the gravitational potential energy to the initial kinetic energy:
KE = PE
1/2 * m * v^2 = m * g * h
Where m is the mass of the cylinder, v is its initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height at which the cylinder stops.
In this case, the mass of the cylinder is not given, but we can still calculate the height at which it stops using the given information. The angle of the incline (20°) and the initial velocity (10 m/s) allows us to calculate the final height using trigonometry:
h = (v^2 * sin^2(θ)) / (2 * g)
Substituting the values into the equation:
h = (10^2 * sin^2(20°)) / (2 * 9.8) ≈ 12.7 m
Therefore, the solid cylinder travels approximately 12.7 meters up the incline.