## anonymous 4 years ago Can someone please help me out with this problem: An object is thrown vertically upward and has a speed of 24m/s when it reaches two thirds of its maximum height above the launch point. Determine its maximum height. Please show me how to do this. Thanks in advance.

1. anonymous

are u there?

2. TuringTest

the velocity at the top is 0 we can use that to set up a kinematic equation for the last third of the motion upwards$v_f^2=v_i^2+2ad$acceleration is g (down) the initial velocity is given, the final velocity is 0, and the height it moves is one-third the total height h/3$0=v_i^2-\frac23gh$solve for h

3. anonymous

hey eash more help me in my question

4. anonymous

Thanks for your help. What happened to the 2, that would be in front of the g?

5. TuringTest

it's still there, but I put it over the three we get from h/3

6. anonymous

ok, what happened to the 2 in 2/3 go?

7. TuringTest

|dw:1328243865207:dw|we are just considering the last third of its flight over the distance h/3 after that if we find h we know the total height

8. anonymous

okay that helped a lot.

9. TuringTest

$v_f^2=v_i^2+2ad$$d=\frac h3$$a=-g$$v_f=0$so we get$0=v_i^2-2g\cdot\frac h3=v_i^2-\frac23gh$