To determine how far the mother can push the baby carriage, we need to calculate the displacement using the given force, angle, and work done.
The work done (W) is given as 2920 J, which is equal to the product of the force (F) and the displacement (d) along the direction of the force:
W = F * d * cos(θ)
Where: W = Work done (2920 J) F = Force applied (62.0 N) d = Displacement θ = Angle between the force and the horizontal (30.0º)
Rearranging the equation, we can solve for the displacement:
d = W / (F * cos(θ))
Substituting the given values:
d = 2920 J / (62.0 N * cos(30.0º))
Using the trigonometric identity cos(30.0º) = √3 / 2:
d = 2920 J / (62.0 N * √3 / 2)
Simplifying further:
d = (2920 J * 2) / (62.0 N * √3) d = 5840 J / (62.0 N * √3)
Evaluating the numerical result:
d ≈ 26.79 meters
Therefore, the mother can push the 20.0 kg baby carriage approximately 26.79 meters.