Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?
A)t = 0.
B)t = .
C)t = .
D)t = .
E)t = .

Question

Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?
A)t = 0. 
B)t = . 
C)t = . 
D)t = . 
E)t = .

Quizplus · Accepted Answer

Let the time at which they pass each other be t seconds. In that time, the outer car would have traveled an angle of ωt and the inner car would have traveled an angle of 3ωt. Since they start in line, we have:

ωt = 2πn    (where n is an integer, as the outer car completes a full revolution)
3ωt = 2πm   (where m is an integer, as the inner car completes three full revolutions)

Solving for t, we get:

t = (2πn)/ω = (2πm)/(3ω)

Multiplying and simplifying, we get:

6mn = π^2

Since m and n are integers, the only solution for this equation is:

m = 57
n = 305

Thus, the time at which they next pass each other is:

t = (2πm)/(3ω) = 11ea7ff9_2b11_9c04_a768_650a46a12e5d_TB2295_11.

Therefore, the answer is C only.

Two People Are on a Ride Where the Inside Cars