Answer:
h=23.67 m : Building height
Explanation:
The rock describes a parabolic path.
The parabolic movement results from the composition of a uniform rectilinear motion (horizontal ) and a uniformly accelerated rectilinear motion of upward or downward motion (vertical ).
The equation of uniform rectilinear motion (horizontal ) for the x axis is
:
x = xi + vx*t Equation (1)
Where:
x: horizontal position in meters (m)
xi: initial horizontal position in meters (m)
t : time (s)
vx: horizontal velocity in m/s
The equations of uniformly accelerated rectilinear motion of upward (vertical ) for the y axis are:
y= y₀+(v₀y)*t - (1/2)*g*t² Equation (2)
vfy= v₀y -gt Equation (3)
Where:
y: vertical position in meters (m)
y₀ : initial vertical position in meters (m)
t : time in seconds (s)
v₀y: initial vertical velocity in m/s
vfy: final vertical velocity in m/s
g: acceleration due to gravity in m/s²
Data
v₀ = 12.2 m/s , at an angle α=53° above the horizontal
x= 25 m , y=0
Calculation of the time it takes for the ball to hit the ground
We replace data in the equation (1)
x = xi + vx*t
x= 25 m ,xi=0 , vx= v₀*cosα = (12.2 m/s)*cos(53°) =7.34 m/s
25 = 0 + 7.34*t
t= 25 / 7.34
t= 3.406 s
Calculation of the Building height
v₀y = v₀*sinα = (12.2 m/s)*sin(53°) = 9.74 m/s
in t= 3.406 s, y=0
We replace data in the equation (2)
y= y₀ + (v₀y)*t - (1/2)*gt²
0= y₀ + (9.74)*(3.406 )- (1/2)*(9.8)(3.406 )²
0= y₀ + 33.17- -56.84
0= y₀ - 23.67
y₀ = 23.67 m =h: Building height
