Jump to level 1 A child is trying to push a wagon full of dirt up a hill. The force the child exerts on the wagon is \( \mathbf{F}_{c}=[190,-130,110] \). The wagon is moving along a path with displacement vector \( \mathbf{d}=[4,-6,1] \). The force of gravity on the wagon is is \( \mathbf{F}_{g}=[0,0,-400] \). What is the magnitude of the total force on the wagon in the direction of motion? Force on wagon \( =1.2 \) In which direction does the wagon move \( \left\{\begin{array}{l}\checkmark \text { Select } \\ \text { Wagon does not move } \\ \text { Wagon moves down the hill } \\ \text { Wagon moves up the hill }\end{array}\right. \) Check

To understand the force exerted on the wagon and the motion involved, it's important to analyze it with a bit of historical context. The principles of forces and motion trace back to Sir Isaac Newton in the 17th century, who established foundational concepts in physics. Newton's laws explain how forces interact and are essential in analyzing real-world scenarios like this one where a child pushes a wagon uphill against gravitational forces. Now, concerning the problem at hand, one common mistake is neglecting the angle of the force's displacement. Ensure you're calculating the component of the applied force in the direction of the displacement vector. The dot product of the child’s force and the displacement will reveal how much of that force is effectively moving the wagon. In this case, since the child’s force is not entirely directed uphill, it might actually be contributing to a downward or neutral motion. So, always visualize the vectors to avoid confusion!