A particle of mass m is projected up from the bottom of an inclined plane with initial velocity V₀ at angle 45° with an inclined plane of inclination 30° as shown in figure. At the same time a small block of same mass m is released along inclined plane from rest at a height h, the particle hits the block at some point on the inclined plane. Neglect friction at inclined. The value of height h is V₀²/(g√a), find a.
Physics · Mixed Chapter
JEE Mains

Question

A particle of mass m is projected up from the bottom of an inclined plane with initial velocity V₀ at angle 45° with an inclined plane of inclination 30° as shown in figure. At the same time a small block of same mass m is released along inclined plane from rest at a height h, the particle hits the block at some point on the inclined plane. Neglect friction at inclined. The value of height h is V₀²/(g√a), find a.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Resolve motion along (∥) and perpendicular (⊥) to the incline. The launched particle has initial components V₀cos45° along the plane and V₀sin45° normal to it. Step 2: Its normal displacement returns to the plane at t=2V₀sin45°/(g cos30°). Step 3: Both the projectile and the block have the same acceleration −g sin30° along the plane. Their relative along-plane acceleration is zero. Thus the projectile's relative travel along the plane is V₀cos45°·t=V₀²/(g cos30°). Step 4: The block star…