PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
Two identical frictionless carts, A and B, each of mass 4.0kg, sit on a straight, horizontal track. Cart B is initially at rest at the origin. Cart A approaches from the left with a speed of 3.0m/s relative to the track. When cart A is 1.0m to the left of the origin, an internal mechanism on A launches a 0.50kg projectile horizontally forward (toward B) with a speed of 6.0m/s relative to cart A at that instant. Neglect air resistance. The projectile is caught by a receptacle on cart B and sticks there without bouncing.
(1) Part 1: (a) In the ground (track) frame, determine the horizontal speed of the projectile immediately after launch.
(2) Part 2: (b) Calculate the time interval between the launch and the instant the projectile lands in cart B.
(3) Part 3: (c) Repeat the analysis for part (b) in a frame that is momentarily at rest with cart A at the instant of launch. Show explicitly how your results match those obtained in the ground frame.
(4) Part 4: (d) Derive an expression for the projectile’s speed relative to cart B at the instant of landing. Then compute its numerical value.
(5) Part 5: (e) Discuss how switching among the three reference frames (ground, cart A rest frame, and cart B rest frame) can simplify different segments of the calculation, and comment on the invariance of the projectile’s acceleration across the inertial frames considered.