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 period of rotation of the outer cars be T. Then the time period of rotation of the inner cars is 1/3 T.

At t = 0, the two cars are in line.

After t seconds, the outer car will have rotated by an angle of ωt and the inner car will have rotated by an angle of 3ωt.

The two cars will next pass each other when the relative angle between them is 180 degrees.

Let's say this happens after time T'. Then we have:

3ωT' - ωT' = π

2ωT' = π

T' = π/2ω

Substituting the value of ω in terms of T, we get:

T' = π/2(T/3)

T' = πT/6

Therefore, the two cars will next pass each other after a time interval of πT/6.

Substituting the numerical value of T from the question, we get:

T' = π/6 seconds

This is approximately equal to 0.524 seconds.

Therefore, the answer is C) t = 11eb6adc_eeac_bf5f_b0cf_c519af5b6b22_TB8245_11.

Two People Are on a Ride Where the Inside Cars