Pls ans ques 3 and 4 - Maths - Introduction to Three Dimensional Geometry

Question

Pls ans ques 3 and 4

Line segments OP, OA and OQ, in the figure above, coincide at the
time t = 0 second At the same instant of time, OP and OQ rotate in
the plane about point O in opposite directions while OA remains
fixed With respect to OA, segment OP rotates at a constant rate of
4°per second and segment OQ rotates at a constant rate of
5° per second

Q3 What is the smallest positive value of t, in seconds, for which
segments OP and OQ will coincide?

Q4 When t = 1 hour, how many more revolutions does segment OQ
complete than segment OP?
Pls ans ques 3 and 4

Muskaan Talwar · Accepted Answer

Dear Student,

Angle covered by OP in 1 second=4°Angle covered by OP in t seconds=4t°Angle covered by OQ in 1 second=5°Angle covered by OQ in t seconds=5t°Since OP and OQ moves in opposite direction,∴4t+5t=360(adding two angles because they are approaching each other, and total angle of circle=360°)⇒9t=360⇒t=3609=40Thus t=40 seconds when they coicide each other
When t=1 hour=60 secondsOP covers=4t=4×60=240°OQ covers=5t=5×60=300°Thus OQ covers 60° more than OP

Regards