Solve for Building Height: Kinematics & Pythagorean Theorem

AI Thread Summary
To determine the height of the building from which a rock is projected, the problem involves using kinematics and the Pythagorean Theorem. The rock has an initial velocity of 7.82 m/s at an angle of 56 degrees, and it lands 10.5 m from the base. The vertical component of the initial velocity must be calculated using the formula Vy = Vo * sin(θ). After finding the initial vertical velocity, kinematic equations can be applied to find the final vertical velocity and subsequently the height of the building. The solution requires careful manipulation of these equations to isolate and solve for the height.
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Homework Statement


A 0.21 kg rock is projected from the edge of
the top of a building with an initial velocity of
7.82 m/s at an angle 56 above the horizontal.
Due to gravity, the rock strikes the ground at
a horizontal distance of 10.5 m from the base
of the building.

How tall is the building? Assume the
ground is level and that the side of the build-
ing is vertical. The acceleration of gravity is
9.8 m/s2 .
Answer in units of m.


Homework Equations



Kinematics equations. Pythagorean Theorem: A +B = C

The Attempt at a Solution



i tried to think about what I needed, and what equation would help me find it. In this case, the height h, I chose the following equation:

H = Vy - VoY / 2A from the initial kinematics equation of Vy = Voy + 2AH

From here, however, I am unsure how to determine Vy, which is the only variable I would need.
 
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All those variables in the exponent section should have exponents of 2 themselves.
 


Vy = vsin \Theta
 


You'll have to split your initial velocity into x and y components. (Use the Pythagorean theorum, your initial velocity will be the hypotenuse.)

Once you've established what the initial y-velocity is, use your kinematics equations to find the final y-velocity. ( vf = vi + a*t )
 
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