1. What is the horizontal distance x between the two balloons

The two hotair balloons in the drawing are 43.2 rn and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3\" above the horizontal. What is the horizontal distance xbetween the two balloons? An aerialist on a high platform holds onto a trapeze attached to- a support by an 7.9m cord. {See the drawing.) Just before heju mps off the platform, the cord makes an angle of 42 with the vertical. Heju mps, swings down, then back up, releasing the trapeze at the instant it is 0.82 rn below its initial height. Calculate the angle 9 that the trapeze cord makes with thevertical at this instant. Two workers are trying to move a heavy crate. One pushes on the crate with a force 31?,which has a magnitude of 222 newtons {N} and is directed due west. The other pusheswith a force '3' , which has a magnitude of 131 N and is directed due north. What are {a} the magnitude and (b1 direction of the resultant force :4? + 3; applied to the crate?Suppose that the second workerapplies a force '3' instead of '3' . What then are {c} the magnitude and {d} direction ofthe resultantforce ] '3' applied to the crate? In both cases express the direction as a positive angle relative to due west. The drawing shows a triplejump on a checkerboard, starting at the center of square A and ending on the center of square B. Each side of a square measures 4.1 cm. What is the magnitude of the displacement of the colored checker during the triplejump [there is only one right corner}? _} The magnitude of a force vector F is 83.5 newtons {N}. The 3: component of this vector is directed along the +x axis and has a a magnitude of 71.3 N. The ycomp-onent points along the +y axis. la} Find the angle between F and the Hi axis. [b] Find the component a of F along the +1; axis- Two geological eld teams are working in a remote area. A global positioning system {GPS} tracker at their base camp shows the location of the rst team as 38.0 km away, 2013'": north of west, and the second team as 34.0 km away, 400 east of north. When the rst team uses its GPS to check the position of the second team,what does it give for the second team's {a} distance from them and lb} direction, measured from due east