A rope, under a tension of 234 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by y = (0.222 m)sin(πx/6.00)sin(12.0πt) where x = 0 at one end of the rope, x is in meters, and t is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
![A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. The player's foot is in contact with the ball for 1.30×10−3 s, and the force of the kick is given by F(t) = [(6.68×105)t − (5.14×108)t2] N for 0 ≤ t ≤ 1.30×10−3 s, where t is in seconds. Find the magnitudes of the following: (a) the impulse on the ball due to the kick, (b) the average force on the ball from the player's foot during the period of contact, (c) the maximum force on the ball from the player's foot during the period of contact, and (d) the ball's speed immediately after it loses contact with the player's foot. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (d) Number Units](https://www.doubtrix.com/uploads/editor/9236055826UBUkTxvDIR.jpg)
