Answer:
The building is 61.19 m tall, approximately.
Explanation:
From the parabollic movement trayectory equation,
[tex]y=H+\frac{v_{0y}}{v_x}x-\frac{1}{2v_x^2}gx^2,[/tex]
where H is the initial height of the ball and [tex]v_{oy}[/tex] and [tex]v_x[/tex] the inital velocities in the vertical and horizontal direction, respectively; we have
[tex]H=y-\frac{v_{0y}}{v_x}x+\frac{1}{2v_x^2}gx^2[/tex].
In this case, the ball landed at the coordinates [tex]\left(x,y\right)=\left(61,0\right)[/tex], so
[tex]H=0-\frac{17\sin\left(43\deg\right)}{17\cos\left(43\deg\right)}\times 61+\frac{1}{2\left(17\cos\left(43\deg\right)\right)^2}\times 9.81\times 61^2 \approx 61.19[/tex].
