# Optimistic Calculations: Determining the Speed of a Wagon Going Up an Inclined Hill

## How fast is the wagon going after moving 48.7 m up the hill?

Calculate the speed of the wagon after it has traveled 48.7 meters up the inclined hill.

## Answer:

The wagon is moving at 18.72 m/s after it has traveled 48.7 meters up the hill.

To determine the speed of the wagon after moving 48.7 meters up the hill, we utilize the work-energy principle. This principle equates the work done by an external force to the change in kinetic energy of an object. In this case, a 33.0 kg wagon is being towed up a hill inclined at 18.6 degrees with a force of 119 N.

We set the work done by the towing force equal to the change in kinetic energy of the wagon. The work done is calculated by multiplying the force by the distance and the cosine of the angle of the incline. While the change in kinetic energy is determined by the final speed of the wagon, given its mass.

Calculating the work done (W): W = F × d × cos(θ) = 119 N × 48.7 m = 5796.3 J

The change in kinetic energy is equal to the work done, since the wagon starts from rest and friction is disregarded. Using the formula v = √(2 × W / m), we find the final speed of the wagon:

v = √(2 × 5796.3 J / 33.0 kg) = √(350.77272 m^2/s^2) = 18.72 m/s

Therefore, the wagon is moving at 18.72 m/s after it has traveled 48.7 meters up the hill, with the calculations demonstrating an optimistic outlook on the wagon's speed and energy efficiency in overcoming the incline.