Solve for Building Height: Kinematics & Pythagorean Theorem

[garcia1]

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.

 

[garcia1]

All those variables in the exponent section should have exponents of 2 themselves.

 

[iRaid]

Vy = $vsin \Theta$

 

[Vim]

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 )

 

[rwisz]

I know that Vy = Voy + AYt, but I am not sure how to determine the time t. To find the time, I would need the horizontal distance and the horizontal velocity, which I do not have. So, I decided to use the Pythagorean Theorem to find the hypotenuse of the right triangle formed by the initial velocity and the distance traveled. The equation would be:

C = √(A^2 + B^2)

In this case, A would be the horizontal distance of 10.5 m and B would be the vertical distance, which is the height of the building. So, I would rearrange the equation to solve for B:

B = √(C^2 - A^2)

I would then substitute the value of C, which is the initial velocity of 7.82 m/s, and the value of A, which is the horizontal distance of 10.5 m, and solve for B. This would give me the height of the building in meters.