1. Sep 10, 2007

### jperk980

1) A lead ball is dropped into a lake from a diving board 5.12 m above the water. It hits the water with a certain velocity and then sinks to the bottom with this same constant velocity. It reaches the bottom 4.72 s after it is dropped. (Assume the positive direction is upward.) How deep is the lake?
For this question I dentified the velocity at which the ball hits the water and that is 10.02 m/s. To get that i used the formula v^2=Vi^2+2ax. I used vi=0, 9.8=a x=5.12. I do not know what to do know because i keep getting the wrong answer and its not off by like like 1 or 2 its off by 10.

2) An object falls from height h from rest and travels 0.46h in the last 1.00 s.
Find the time of its fall.
Find the height of its fall.
For this one I believe i should use the formula x=vt-.5at^2. I know believe time is t-1 and the hieght is h-.46. Could you please help me understand what i should do next becuase i am clueless how to put this information into a formula.
Thank you for the help

2. Sep 10, 2007

### Staff: Mentor

So far, so good.
Start by figuring out how long it takes for the ball to hit the water. Then figure out how much time it spends in the water.

3. Sep 10, 2007

### Staff: Mentor

That will work, using down as positive and thus D = 0.5gt^2. But you need to apply it twice: once for the distance h-.46h and once for the distance h.

Correction: The first position given is .46h, not .46; so the distance fallen is h-.46h.

Last edited: Sep 10, 2007
4. Sep 10, 2007

### jperk980

i dont understand what your saying by using twice how would i put that into a formula and how would i solve for t and h because there would be 2 varibles in that equation you gave me

5. Sep 10, 2007

### jperk980

btw thanks for your help with the first problem it made it a lot easier for me to solve

6. Sep 10, 2007

### Staff: Mentor

Since you have two variables you need two equations. Write one equation for the distance h-.46h & time t-1; write another equation for the distance h and time t. You'll need to solve them together to find h & t.

(See my correction to post #3.)

Last edited: Sep 10, 2007
7. Sep 10, 2007

### jperk980

okay i do that and i come up with the equations h=.5*9.8*t^2 and h-.46h=.5*9.8*(t-1)^2 so now what do i do with that is there a way to set them equal and solve for t because i cant figure out how to do that

8. Sep 11, 2007

### Staff: Mentor

One way to solve these simultaneous equations is to substitute one into the other. Replace "h" in the second equation with .5*9.8*t^2 from the first equation. Then you can solve the quadratic equation for t. (And then plug in to get h.)

9. Sep 11, 2007

### jperk980

Thanks Doc Al for all your help. I finally got the answer. Thanks so much.