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Physics: 2D Kinematics

A rock is thrown horizontally at a speed of 80ft/sec from the top of a building that is 64 ft high.

A) How long does it take for the rock to hit the land?

B) How far from the base of the building will the rock land?

C) At what speed does the rock hit the land?

My answers so far are:
a) t = 1.995 seconds to hit ground
b) rock will land 48.68 meters (or 159.62 feet) away from the base of the building
c) Haven't finished solving but I keep getting v^2 = -358.68 m/s which is impossible... Unless it means 358 m/s in the opposite direction, which DOES make sense, since velocity is a vector which has direction and magnitude.
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Zenoture
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Zenoture
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2 Solutions
 
ozoCommented:
with what vertical velocity will the rock hit the land?
with what horizontal velocity will the rock hit the land?
or
with what kinetic energy will the rock hit the land?
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ZenotureAuthor Commented:
Don't think I'm allowed to use KE since this is for my multivariable calc class, but vert. velocity is v*sin(@), and horizontal velocity is v*cos(@), but we know vo = <24.4, 0> making our vo[x] = 24.4
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ozoCommented:
How did you get v^2 = -358.68 m/s?
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ZenotureAuthor Commented:
v^2 = vo^2 - 2gd

But after revising what I had and thinking simple, I realized that Vx is constant, since ax = 0, therefore Vfx = Vox = 24.4 m/s

Vfy = Voy - gt = 0 - (9.8)*(1.99) = -19.50 j

|| Vf || = sqrt( Vfx^2 + Vfy^2 ) = 31.23 m/s
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ozoCommented:
That makes more sense than sqrt(-358.68 m/s)
which would have units of i*sqrt(m)/sqrt(s)

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ZenotureAuthor Commented:
The full work out is shown in my answer, but was arrived at by the help of ozo.
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