Final answer:
To calculate the time it takes for the wagon to reach a speed of 4.50 m/s, we can use Newton's second law of motion. By resolving the forces acting on the wagon and using the relevant formulas, we can calculate the acceleration and then use the kinematic equation to find the time taken.
Step-by-step explanation:
To calculate the time it takes for the wagon to reach a speed of 4.50 m/s, we can use Newton's second law of motion. First, let's resolve the forces acting on the wagon. The force exerted by the girl is 15.0 N at an angle of 20.0 degrees with the horizontal. We can find the horizontal component of this force by multiplying the force by the cosine of the angle. So, the horizontal component is 15.0 N * cos(20.0°). The frictional force is given as 11.0 N in the opposite direction. The net force on the wagon is the sum of the horizontal component of the force exerted by the girl and the frictional force, which is (15.0 N * cos(20.0°)) - 11.0 N.
Now, we can use Newton's second law, which states that the net force is equal to the mass of the object multiplied by its acceleration. In this case, the net force is (15.0 N * cos(20.0°)) - 11.0 N, and the mass of the wagon is 12.0 kg. We can rearrange the formula to solve for the acceleration of the wagon: acceleration = net force / mass.
Once we have the acceleration, we can use the kinematic equation v = u + at to find the time taken. In this equation, v is the final velocity (4.50 m/s), u is the initial velocity (0 m/s), a is the acceleration, and t is the time taken. Rearranging the equation gives us t = (v - u) / a. Substituting the known values gives us the time taken for the wagon to reach a speed of 4.50 m/s.