Discussion_8_Rewrite

Physics 1A Discussion Week 8 Due Wednesday 05/25/22 at 11:59pm on Gradescope — NO LATE SUBMISSIONS NO LATE SUBMISSIONS ACCEPTED FOR THIS ASSIGNMENT SO SOLUTIONS CAN BE RELEASED PRIOR TO MIDTERM 2 Problem 1 A projectile of mass M is launched directly upwards with an initial speed of v 0 = 20 m/s. At its peak height it breaks into two parts with m 1 = 2 M /3 and m 2 = M /3, and just after it breaks you measure that m 1 is traveling at a speed of v 1 = 1 m/s directly horizontally. a) How far apart are m 1 and m 2 when they land? b) Where is the center of mass of the system when m 1 and m 2 have landed? Problem 2 a) Calculate the final momentum vector for a perfectly elastic collision between two particles if their masses are given by m 1 = 0.5 kg, and m 2 = 0.25 kg, and their velocities the moment before collision are . b) If m 1 is seen to be moving along the positive x- axis just after the collision what are the final speeds of the particles? c) Calculate the angle between the final velocity of particle 2 and the x -axis. Problem 3 A ball of unknown mass is thrown at a nearby target of mass M = 0.5 kg that is attached to a spring with spring constant k = 100 N/m. You measure the speed of the ball to be 10 m/s just before impact with the target. After the collision the spring's maximum compression is measured to be 0.1 m. What is the mass of the ball if: a) the ball is made of putty (assume a perfectly inelastic collision, and ignore any deflection of the ball due to gravity)? b) the ball is made of a hard material that bounces off of the target (assume a perfectly elastic collision and no loss of energy)? ⃗ v 1 = (2 ̂ i + 1 ̂ j ) m/s and ⃗ v 2 = ( − 4 ̂ i + 2 ̂ j ) m/s