Calculating Velocity and Time of a Horizontal Projectile

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A rock is thrown horizontally from a 50m building, landing 70m from the base, and the time in the air is calculated to be approximately 3.194 seconds. The vertical motion is analyzed using the equation for displacement, where the height of 50m is set equal to half the acceleration due to gravity multiplied by the square of the time. The horizontal velocity is then derived from the horizontal distance traveled, but there are difficulties in solving for it correctly. The key point is that the vertical motion is independent of the horizontal motion, simplifying the calculations. The discussion emphasizes the importance of correctly applying kinematic equations for both vertical and horizontal components.
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Homework Statement



A person throws a rock horizontally from the roof of a 50m building. The rock lands 70 m from the base of the building.
How long was the rock in the air in s?

I got 3.194. The online home work thingy (webassign) said I was right.

With what velocity was the rock thrown in m/s?


Homework Equations


I used the Xf equation and solved for time. Dont I just plug in the time i got in the last equation and actualy solve it? Well i tryed that but I just keep getting it wrong.


The Attempt at a Solution


70=-4.9(3.194)^2 + Vo(3.194) Is this right?
 
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The way you need to set it up is imagine the rock is simply dropping because the x velocity doesn't matter. So s = vt + 1/2 at^2 s = 50m v = 0 a = 9.8m/s^2
 
50 = 0t + 1/2 9.8 t^2
 
djeitnstine said:
The way you need to set it up is imagine the rock is simply dropping because the x velocity doesn't matter. So s = vt + 1/2 at^2 s = 50m v = 0 a = 9.8m/s^2
what does s represent in this?
 
I think i did my algebra wrong because it said it was wrong.

(49.88+50)/3.194= 31.305
 
sorry s is displacement
 
50 = 0t + 1/2 9.8 t^2 this is the equation, the height 50 is equal to zero plus 1/2 9.8*t^2 (the rock is modeled as only dropping from 50 meters above the ground the x velocity has nothing to do with it)
 

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