A horizontal crane arm is mounted on a pivot point on the top of a vertical tower (the mass of the crane arm itself is negligible). A 500kg load is hanging from the right end of the arm, 30m to the right of the tower. Where on the arm must the 24,000kg counterweight be placed in order for the arm to be balanced (static equilibrium)?

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.