Answer:

Explanation:
The textbooks say that the maximum range for projectile motion (with no air resistance) is 45 degrees.
Answer:
a) see attached, a = g sin θ
b)
c) v = √(2gL (1-cos θ))
Explanation:
In the attached we can see the forces on the sphere, which are the attention of the bar that is perpendicular to the movement and the weight of the sphere that is vertical at all times. To solve this problem, a reference system is created with one axis parallel to the bar and the other perpendicular to the rod, the weight of decomposing in this reference system and the linear acceleration is given by
Wₓ = m a
W sin θ = m a
a = g sin θ
b) The diagram is the same, the only thing that changes is the angle that is less
θ' = 9/2 θ
c) At this point the weight and the force of the bar are in the same line of action, so that at linear acceleration it is zero, even when the pendulum has velocity v, so it follows its path.
The easiest way to find linear speed is to use conservation of energy
Highest point
Em₀ = mg h = mg L (1-cos tea)
Lowest point
Emf = K = ½ m v²
Em₀ = Emf
g L (1-cos θ) = v² / 2
v = √(2gL (1-cos θ))
Answer:
d=360 miles
Donna lives 360 miles from the mountains.
Explanation:
Conceptual analysis
We apply the formula to calculate uniform moving distance[
d=v*t Formula (1)
d: distance in miles
t: time in hours
v: speed in miles/hour
Development of problem
The distance Donna traveled to the mountains is equal to the distance back home, equal to d,then,we pose the kinematic equations for d, applying formula 1:
travel data to the mountains: t₁= 8 hours , v=v₁
d= v₁*t₁=8*v₁ Equation (1)
data back home : t₂=4hours , v=v₂=v₁+45
d=v₂*t₂=(v₁+45)*4=4v₁+180 Equation (2)
Equation (1)=Equation (2)
8*v₁=4v₁+180
8*v₁-4v₁=180
4v₁=180
v₁=180÷4=45 miles/hour
we replace v₁=45 miles/hour in equation (1)
d=8hour*45miles/hour
d=360 miles