There are 3 different highways from City W to City X, 4 different highways from City X to
City Y, and 3 different highways from City Y
to City Z. How many different routes are there
for a trip from City W to City X to City Y to
City Z?

6 x 4 you have 4 numbers and each can be put in 6 different ways. so it is 24 i think

Step-by-step explanation:

ω = √((3g/L)*(1 - Cos θ))

Step-by-step explanation:

We need to apply the Principle of Conservation of mechanical energy as follows

Ei = Ef    ⇒ Ki + Ui = Kf + Uf

In the vertical position

ωi = 0 ⇒ Ki = 0

yi = L/2 ⇒ Ui = m*g*L/2

We can get the rotational inertia I using the formula

I = m*L²/3

then

Kf = I*ω²/2 = (m*L²/3)*ω²/2 = m*L²*ω²/6

Now, we obtain the potential energy Uf as follows

Uf = m*g*y

where

y = (L/2)*Cos θ

⇒ Uf = m*g*(L/2)*Cos θ

Now, we have

Ui = Kf + Uf

⇒ m*g*L/2 = (m*L²*ω²/6) + (m*g*(L/2)*Cos θ)

⇒ ω² = (3g/L)*(1 - Cos θ)

⇒ ω = √((3g/L)*(1 - Cos θ))

We need to know the coefficient of static friction in order to get the value of theta where slip takes place.