A cat runs along a straight line with constant velocity of magnitude v = 5 m/s. A dog chases the cat such that the velocity of dog is always directed towards the cat. The speed of dog is u = 6 m/s and is always constant. At an instant, both are separated by distance x = 10 metres and their velocities are mutually perpendicular. Find the magnitude of acceleration of dog in m/s² at that instant.
Physics · Mixed Chapter
JEE Mains

Question

A cat runs along a straight line with constant velocity of magnitude v = 5 m/s. A dog chases the cat such that the velocity of dog is always directed towards the cat. The speed of dog is u = 6 m/s and is always constant. At an instant, both are separated by distance x = 10 metres and their velocities are mutually perpendicular. Find the magnitude of acceleration of dog in m/s² at that instant.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The dog always heads along the line joining it to the cat at constant speed u=6 m/s. At the instant shown, the cat's velocity 5 m/s is perpendicular to this line, which is 10 m long. Step 2: The line of sight rotates at angular rate ω=vₚₑᵣₚ/x=5/10=0.5 rad/s. Step 3: Since the dog's velocity direction rotates at ω while its speed remains 6, its acceleration magnitude is a=uω=6×0.5=3 m s⁻².