Answer:
maximum height above point kicked 8.2 m
Step-by-step explanation:
With we have a friction force, let's use Newton's second law to find the acceleration of the body, let's look at the diagram in the attacment
-fr -W sin θ = m a
N - W cos θ = 0 ⇒ N = mg cos θ
The equation for the force of friction is fr = μN, substitute and calculate
-μ (mg cos θ) - mg sin θ = ma
-μ g cos θ- g sin θ = a
a = -g (μ cos θ + sin θ)
a = - 9.8 (0.395 cos 37.5 + sin 37.5)
a = - 9.04 m/s²
The negative sign indicates that the acceleration is stopping the movement.
With this acceleration we can calculate the speed of the stone when it reaches the end of the roof
Vf² = Vo² - 2 to Y
The distance of 10 m is along the ceiling, let's calculate with trigonometry when the height rises
sin θ=Y / L ⇒ Y = L sin θ
Y = 10.0 sin 37.5
Y = 6 m
Let's replace and calculate the speed
Vf = √(15 2 - 2 9.04 6)
Vf = 10.8 m / s
This is the speed with which the stone reaches the end of the roof, from where its parabolic movement begins, where is the initial velocity Vo = 10.8 m/s with the roof angle T = 37.5º. Let's calculate the maximum height reached at this point the vertical speed must be zero (Vy = 0)
Let's look for trigonometry the components of the initial velocity
Vox = Vo cos θ
Voy = Vo sin Tθ
Vox = 10.8 cos 37.5
Voy = 10.8 sin 37.5
Vox = 8.33 m / s
Voy = 6.57 m / s
Let's calculate the maximum height
Vyf² = Voy² - 2 g Y
0 = Voy2 - 2 g Y
Y = Voy² / 2g
Y = 6.57²/2 9.8
Y = 2.2 m
This is the maximum height from the tip of the roof
Measured from the point where the stone was kicked we must add the height of advanced on the roof
Y = Y roof + Y max
Y = 6 + 2.2
Y = 8.2 m
This is the height measured from the point where it was kicked