Three small snails are each at a vertex of an equilateral triangle of side 6 meter. The first sets out towards the second, the second towards third and thirds towards the first with a uniform speed of 5 cm min⁻¹. During their motion each of them always heads towards its respective target. How much distance is covered by each snail before they meet (in meter)
Physics · Mixed Chapter
JEE Mains

Question

Three small snails are each at a vertex of an equilateral triangle of side 6 meter. The first sets out towards the second, the second towards third and thirds towards the first with a uniform speed of 5 cm min⁻¹. During their motion each of them always heads towards its respective target. How much distance is covered by each snail before they meet (in meter)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The three snails always form a shrinking, rotating equilateral triangle by symmetry; the direction to the target makes 30° with the inward radius to the centroid. Step 2: The initial distance of a vertex from the centroid is R₀=a/√3=6/√3 m. Step 3: The inward component of each snail's constant speed v is v cos30°=v√3/2. Time to meet is t=R₀/(v√3/2). Step 4: Distance each covers =vt=R₀/cos30°=(6/√3)/(√3/2)=4 m. Answer: 4.