6) Consider the equation v ? 13 zxt 2

6) Consider the equation v ? 13 zxt 2. The dimensions of the variables v, x, and t are [L]/[T], [L], and [T], respectively. The numerical factor 3 is dimensionless. What must be the dimensions of the variable z, such that both sides of the equation have the same dimensions? Show how you determined your answer. 10. A partly full paint can has 0.67 U.S. gallons of paint left in it. (a) What is the volume of the paint in cubic meters? (b) If all the remain- ing paint is used to coat a wall evenly (wall area ? 13 m2), how thick is the layer of wet paint? Give your answer in meters. 16. The drawing shows a person looking at a building on top of which an antenna is mounted. The horizontal distance between the person’s eyes and the building is 85.0 m. In part a the person is looking at the base of the antenna, and his line of sight makes an angle of 35.0? with the horizontal. In part b the person is looking at the top of the antenna, and his line of sight makes an angle of 38.0? with the horizontal. How tall is the antenna? 22. An aerialist on a high platform holds on to a trapeze attached to a support by an 8.0-m cord. (See the drawing.) Just before he jumps off the platform, the cord makes an angle of 41? with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.75 m below its initial height. Calculate the angle ? that the trapeze cord makes with the verti- cal at this instant. 36. Soccer player #1 is 8.6 m from the goal (see the drawing). If she kicks the ball directly into the net, the ball has a B displacement labeled A. If, on the other hand, she first kicks it to player #2, who then kicks it into the net, the ball undergoes two successive dis- placements, BA and BA . What are the yxB magnitudes and directions of Ax and BAy? 46. The three displacement vectors in the drawing have magnitudes of A ? 5.00 m, B ? 5.00 m, and C ? 4.00 m. Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis.