## anonymous one year ago PROJECTILE MOTION A bartender slides a beer mug at 1.50 m/s towards a customer at the end of a frictionless bar that is 1.20 m tall. The customer makes a grab for the mug and misses, and the mug sails off the end of the bar. a) How far away from the end of the bar does the mug hit the floor? b) What are the speed and direction of the mug at impact?

1. anonymous

I've answered Part A, and I got 0.75 m.

2. anonymous

I'll show the work in a minute or two.

3. Michele_Laino

the velocity has two components: 1) the horizontal component whose magnitude is 1.50 m/s 2) the vertical component whose magnitude is: $\sqrt {2gh} = \sqrt {2 \cdot 9.81 \cdot 1.2} = ...?$

4. anonymous

I first found $$t$$. $\Delta y=V_0y t+ \frac{1}{2}at^2$$-1.2= -4.9t^2$$$t=0.5s$$ Then I found for $$\Delta x$$/. $\Delta x=V_0xt$$\Delta x=(1.50)(0.5)$$\Delta x=0.75m$

5. Michele_Laino

|dw:1444181078166:dw|

6. anonymous

Wait, so should I find the y component first using the formula you showed or that's for the velocity?

7. Michele_Laino

since your mug, at impact, gains a vertical speed

8. anonymous

And I got 5.077 m/s.

9. anonymous

or 5.08 m/s

10. Michele_Laino

I got a different result: $\sqrt {2gh} = \sqrt {2 \cdot 9.81 \cdot 1.2} = 4.85$

11. Michele_Laino

do you agree?

12. anonymous

No, because that's just the y component, and what I did it I found the y component (4.85) and the x component (1.5), then I used $$v=\sqrt {(4.85)^2+(1.5)^2}$$.

13. Michele_Laino

ok! your answer is correct, I meant the vertical speed is 4.85

14. anonymous

Ohh I was thinking ahead. Then to find the direction, should l just use tan^-1 V_fy/V_fx?

15. anonymous

which gives me 72.81 degrees.

16. Michele_Laino

correct! for direction we can write this: $4.85 = 1.5 \cdot \tan \theta$ |dw:1444181647493:dw|

17. anonymous

Hold on, it would be negative, right?

18. Michele_Laino

no, since we consider this angle $$\beta=180-72.81=...$$ |dw:1444181805577:dw|

19. Michele_Laino

sorry, you are right, it is -72.81 degree

20. Michele_Laino

|dw:1444181937222:dw|

21. anonymous

Oh okay! It kinda confuses me when I don't see an illustration, but I just thought that since it's dropping, it would be in the IV Quadrant or something.

22. anonymous

Thank you very much for helping me! This means a lot.I hope I'll ace the test tomorrow. :D

23. Michele_Laino

:) :)