# Falling object 1D Kinematic Question

1. Sep 3, 2009

### CandyApples

1. The problem statement, all variables and given/known data
An object falls from height h from rest. If it travels .5h in the last second before hitting the ground, determine how long it takes to fall and the height h.
xi = .5hm, t =1s, a = 9.8m/s^2, xf = 0m,

2. Relevant equations
Vf = Vi + at
xf = xi + .5at^2

3. The attempt at a solution
xf = xi + .5at^2
0 = .5h + .5(-9.8)(1)
h = 9.8m

I know that this answer is not correct, I am having trouble figuring out how to manipulate the given data into one of those equations to either come up with h or find the total time.

2. Sep 3, 2009

### Jebus_Chris

all you need in this problem is
$$x_f = x_i + \frac{1}{2}gt^2$$

A good place to start would be to find h in terms of t.

Also, the object travels .h in the last second which means that the displacement from when the ball hits the ground minus the displacement of where the ball was 1 second ago equals .5h.

3. Sep 3, 2009

### tiny-tim

Hi CandyApples!

(try using the X2 and X2 tags just above the Reply box )
Nooo … learn your constant acceleration equations …

it should be xf = xi + vit + .5at2

(and for that reason, you'll see it's not actually a very helpful equation to use! )

Hint: don't try to do it all in one equation … use two equations, both with vi = 0.

4. Sep 4, 2009

### CandyApples

Ok so trying a different method, I think I am a little closer.

Using the equation Vf2 = 2ax I have determined that Vf = (19.6h)1/2. The problem is that when I use this value for Vf=Vi+at I have two variables (h and t). Is there any way I can find t?

5. Sep 4, 2009

### tiny-tim

Nooo … why have you introduced vf? … you're not asked for it, it only gives you an unwanted extra unknown

Hint: think of it as two projectiles …

you drop them both together from height h, one hits a ledge at height h/2, and the other hits the ground at height 0 one second later.

So for both of them, you have vi a and s, and you have a relationship between t.

What do you get?

6. Sep 4, 2009

### CandyApples

well if i treat them as two separate objects, s = Vit + .5at2 will work to correlate the two by setting one t to either t+1 or t-1, right?

This will work if it is ok to set Vi equal to zero for both equations.

Equation 1 will be h = .5(-9.8)t2
Equation 2 will be .5h = .5(-9.8)(t-1)2

If this is logically set up, it will provide a way to link the two times together to find a numeric answer for h.

7. Sep 4, 2009

### rl.bhat

Now substitute the value of h from the first equation in the second and solve the quadratic to find t. From that value you can find h.

8. Sep 4, 2009

### CandyApples

Wow I got it now, thank you so much :-). I am so slow when it comes to physics.