- #1
hey123a
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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
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