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## Homework Statement

Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.00m. The stones are thrown with the same speed of 9.0m/s. Find the location (above the base of the cliff) of the point where the stones cross paths.

h = 6.00m

v = 9.0m/s

**The answer to the question is**

h = 2.45m

t = 1/3

h = 2.45m

t = 1/3

## Homework Equations

y = Vot + 1/2at^2

## The Attempt at a Solution

Yup = Vot + 1/2at^2

Yup = 9.0t + 1/2(-9.8)t^2

Yup = 9.0t - 4.9t^2

Ydown = h - (Vot + 1/2at^2)

Ydown = 6 - [(-9.0)t + 1/2(-9.8)t^2)]

Ydown = 6 - [-9.0t - 4.9t^2]

Ydown = 6 + 9.0t + 4.9t^2

Cross paths when:

Yup = Ydown

9.0t - 4.9t^2 = 6 + 9.0t + 4.9t^2

-4.9t^2 = 6 + 4.9t^2

-6 = 9.8t^2

t = 0.24999, this is already wrong since the answer for t = 1/3

But I get the right answer for time when I solve this way:

Yup = Ydown

9.0t - 4.9t^2 = 6 - [-9.0t - 4.9t^2]

9.0t = 6-(-9.0t)

18t = 6-0

18t = 6

t = 6/18

t = 1/3

However, when I go to find the height I get different answers:

Ydown = 6 - [-9.0t - 4.9t^2]

Ydown = 6 - [-9.0(1/3) - 4.9(1/3^2)]

Ydown = 3.54444

Yup = 9.0t - 4.9t^2

Yup = 9.0(1/3) - 4.9(1/3^2)

Yup = 2.456

I need help understanding what I'm doing wrong. I've learned that positive values are always objects that move towards the positive x axis or upwards. And I've learned that negative values are always objects that move towards the negative x axis or downwards