Question

A marching band consists of rows of musicians walking in straight, even lines. When a marching band performs in an event, such as a parade, and must round a curve in the road, the musician on the outside of the curve must walk around the curve in the same amount of time as the musician on the inside of the curve. This motion can be approximated by a disk rotating at a constant rate about an axis perpendicular to its plane. In this case, the axis of rotation is at the inside of the curve. Consider two musicians, Alf and Beth. Beth is four times the distance from the inside of the curve as Alf. Knowing that If Beth travels a distance s during time Δt, how far does Alf travel during the same amount of time= (1/4)s

If Alf moves with speed v, what is Beth's speed?

a. 4v
b. v
c. v/4

Answer 1

A) Total distance Alf travel during the same amount of time =
`(1)/(4)s`

B) Speed of Beth = 4v

Step-by-step explanation:

Given - Consider two musicians, Alf and Beth. Beth is four times the

distance from the inside of the curve as Alf.

To find - A) Knowing that If Beth travels a distance s during time Δt, how

far does Alf travel during the same amount of time.

B) If Alf moves with speed v, what is Beth's speed?

Proof -

A)

As we know that

Speed = Distance / Time

⇒Distance = Speed ×Time

Now,

Given Speed of Alf = v

⇒Distance of Alf = vt

Also,

Distance of Beth = Speed of beth×time

Given that

Beth is four times the distance from the inside of the curve as Alf. Knowing that If Beth travels a distance s during time Δt, how far does Alf travel during the same amount of time=

⇒Distance of Alf = Speed of Alf×time

=
`(1)/(4)` Distance of Beth

⇒Distance of Alf =
`(1)/(4)s`

∴ we get

Total distance Alf travel during the same amount of time =
`(1)/(4)s`

B)

We know the conversion of angular velocity

ω(Alf) = ω(Beth)

⇒V(Alf)/ r = V(Beth)/4r

⇒V(Alf) = V(Beth) / 4

⇒V(Beth) = 4 V(Alf)

As given, Alf moves with speed v

⇒V(Beth) = 4v

So, the correct option is - a.4v