NEETPhysicsMotion in One Dimension
A cyclist rides along a highway. A fleet of autonomous delivery pods leaves a depot in both directions every 15 minutes at a constant speed of 60 km/h . The ratio of the time interval between pods overtaking the cyclist to the time interval between pods crossing the cyclist from the opposite direction is 3:1 . What is the cyclist's speed and the exact time interval between opposite-direction encounters?
Options
- A30 km/h , 15 min
- B30 km/h , 10 min
- C20 km/h , 10 min
- D30 km/h , 30 min
Correct answer
B. 30 km/h , 10 min
Step-by-step solution
Let the speed of the cyclist be v_c . The speed of the pods is v_p = 60 km/h . The distance d between consecutive pods in either direction is: d = v_p T = 60 15 60 = 15 km The time interval for pods overtaking the cyclist (same direction) is: t_ overtake = d v_p - v_c The time interval for pods crossing from the opposite direction is: t_ opposite = d v_p + v_c Given the ratio t_ overtake : t_ opposite = 3 : 1 , we have: v_p + v_c v_p - v_c = 3 60 + v_c = 3(60 - v_c) 60 + v_c = 180 - 3v_c 4v_c = 120 v_c = 30 km/h No