The problem you're referring to seems to describe the motion of a 24 kg object falling from a height $h$, with a velocity of 30 m/s when it reaches the ground. The task is to calculate the work done by the forces acting on the object during the fall, and to find the length of the path traveled.

Here's the approach to solve the problem:

1. Work Done by Forces: The work done on the object is the sum of the work done by gravity and any other forces (like air resistance if it's present). We can use the following work-energy theorem:

   $W = \Delta K$

   where $\Delta K$ is the change in kinetic energy.

   $\Delta K = \frac{1}{2} m v^2 - 0$

   where:

   • $m = 24 \, \text{kg}$ (mass of the object),
   • $v = 30 \, \text{m/s}$ (final velocity).

   So, we can calculate the work done by gravity.

2. Length of the Path: To calculate the length of the path traveled, we would use the equation of motion under constant acceleration (assuming no air resistance):

   $v^2 = u^2 + 2gh$

   where:

   • $u = 0 \, \text{m/s}$ (initial velocity),
   • $v = 30 \, \text{m/s}$,
   • $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity),
   • $h$ is the height from which the object falls.

   From this, we can solve for $h$.

Let me calculate these values for you! Given values m = 24 # mass in kg v = 30 # final velocity in m/s g = 9.8 # acceleration due to gravity in m/s^2

Calculate change in kinetic energy (work done by gravity)

K_initial = 0 # Initial kinetic energy is zero since initial velocity is zero K_final = 0.5 * m * v**2 # Final kinetic energy

work_done = K_final - K_initial # Work done by gravity

Calculate the height (h) using the equation v^2 = u^2 + 2gh

u = 0 # Initial velocity h = (v2 - u2) / (2 * g) # Rearranged equation to solve for h

work_done, hThe results are as follows:

1. The work done by gravity on the object is 10,800 J (Joules).
2. The height from which the object falls is approximately 45.92 meters.

Would you like further details or have any other questions on this? Here are some related questions for exploration:

1. How would the work change if air resistance was considered?
2. What would be the velocity of the object just before it hits the ground if it started from a different height?
3. How can you calculate the work done by forces other than gravity?
4. What is the effect of mass on the kinetic energy and work done?
5. How do you determine the acceleration due to gravity at different locations on Earth?

Tip: When calculating the work done in physics problems, always remember to take into account both initial and final energy states.