The height of the building is 53.4 m (projectile motion)
Explanation:
The motion of the ball is a projectile motion, so it follows a parabolic path which consists of two independent motions:  
- A uniform motion (constant velocity) along the horizontal direction  
- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction  
First of all, we consider the horizontal motion, which is a uniform motion at constant speed. The equation that gives the horizontal distance travelled is:
 
  
where:
 is the horizontal velocity of the ball, which is constant since there are no forces in this direction
 is the horizontal velocity of the ball, which is constant since there are no forces in this direction
d = 165 m is the horizontal distance travelled by the ball
Solving for t, we find the time of flight:

Now we analyze the vertical motion: it is an accelerated motion, we can use the suvat equation
 
  
where  
s is the vertical displacement, which is the height of the building
u = 0 is the initial vertical velocity of the ball
t = 3.3 s is the time of flight
 is the acceleration of gravity
 is the acceleration of gravity  
Solving for s, we find the height of the building:

Learn more about projectile motion here:
brainly.com/question/8751410
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