Final answer:
The girl does 39.65 J of work on the wagon in the first 2.0 s. She exerts an instantaneous power of 47.25 W at t = 2.0 s.
Step-by-step explanation:
(a) How much work does the girl do on the wagon in the first 2.0 s?
To calculate the work done by the girl on the wagon, we need to find the displacement of the wagon and the angle between the applied force and the displacement. The work done is given by the equation:
Work = Force * Displacement * cos(θ)
In this case, the force is 10 N, and the displacement can be calculated using the formula for constant acceleration:
Displacement = (1/2) * acceleration * time^2
Since the wagon starts from rest, the initial velocity is 0 m/s. Using the equation of motion, v = u + at, we can find the acceleration:
0 = u + at, where u = 0, a = F / m, and t = 2 s
0 = 0 + (F / m) * 2
F = (m / 2) * a
Substituting the given values, we have:
F = (15 kg / 2) * a
10 N = (15 kg / 2) * a
a = (10 N * 2) / (15 kg)
a = 1.33 m/s^2
Now we can find the displacement:
Displacement = (1/2) * 1.33 m/s^2 * (2 s)^2
Displacement = 5.32 m
Substituting the values into the equation for work:
Work = 10 N * 5.32 m * cos(37°)
Work = 39.65 J
(b) How much instantaneous power does she exert at t = 2.0 s?
The instantaneous power is given by the equation:
Power = Force * velocity * cos(θ)
Using the equation of motion, v = u + at, we can find the final velocity:
v = u + at
v = 0 + 1.33 m/s^2 * 2 s
v = 2.66 m/s
Substituting the values into the equation for power:
Power = 10 N * 2.66 m/s * cos(37°)
Power = 47.25 W