anonymous one year ago a rock dropped from a high platform is moving at 24 m/s downward when it strikes the ground. Ignore air resistance. How fast was the rock moving when it had fallen only one-fourth of the distance to the ground? 8.0 m/s , 6.0 m/s, 18.0 m/s , or 12.0 m/s ? :/

1. Michele_Laino

please wait a moment, since I have to draw a table

2. anonymous

ok!

3. Michele_Laino

I'm pondering....

4. anonymous

ok! :)

5. Michele_Laino

we have the subsequent situation: |dw:1433105987038:dw| so total mechanical energy is: ${E_{TOTAL}} = \frac{1}{2}m{v^2}$ where m is the mass of the ball or the mass of the rock

6. anonymous

yes:)

7. Michele_Laino

the mechanical energy, namely KE+PE has to be constant, during the free falling motion of our rock, and its value has to be equal to E_TOTAL

8. Michele_Laino

so we have this situation: |dw:1433106277846:dw|

9. anonymous

yes:)

10. Michele_Laino

at position P, we can write this equation (energy conservation): $mg\frac{{3h}}{4} + \frac{1}{2}mv_0^2 = {E_{TOTAL}} = mgh$

11. anonymous

ok! what do we plug in?

12. Michele_Laino

dividing both sides by the product m*g, we get: $\frac{{3h}}{4} + \frac{{v_0^2}}{g} = h$

13. Michele_Laino

then we can write: $\begin{gathered} \frac{{v_0^2}}{g} = h - \frac{{3h}}{4} \hfill \\ \hfill \\ \frac{{v_0^2}}{g} = \frac{h}{4} \hfill \\ \hfill \\ v_0^2 = \frac{{gh}}{4} \hfill \\ \end{gathered}$

14. anonymous

how can we solve for that?

15. Michele_Laino

here is the next step: ${v_0} = \sqrt {\frac{{gh}}{4}}$

16. anonymous

ok! what do we plug in?

17. anonymous

would h be 24?

18. Michele_Laino

no, since we have: $h = \frac{{{{24}^2}}}{{2 \times 9.81}} = ...meters$

19. anonymous

ohh okay so we get 29.357?

20. Michele_Laino

ok! h=29.4 meters

21. Michele_Laino

now we have: ${v_0} = \sqrt {\frac{{gh}}{4}} = \sqrt {\frac{{9.81 \times 29.4}}{4}} = ...m/\sec$

22. anonymous

8.49?

23. Michele_Laino

yes! that's right!

24. Michele_Laino

so, what is the right option?

25. anonymous

8.0 m/s?

26. Michele_Laino

that's right!

27. anonymous

yay thanks!!

28. Michele_Laino

:)