11.

Orienteering. In an orienteering class. you have the goal of moving as far {straight-line distance) from base camp as possible by making three straight-line moves. You mayr use the following displacements in am{ order: (a) :1). 2.7 km clue east (directly toward the east); {b} b . 1.1 km 24" north of east [at an angle of 24D toward the north from due east); (c) E) 1.8 km due west. Alternately, you may substitute 4 4) either b for b or ? for 3'. What is the greatest distance you can be from base camp at the end of the third displacement (regardless of direction}? Number n Units v An explorer is caught in a whiteout {in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.4 km. but when the snow clears, he discovers that he actually traveled 8.1 km at 53 north of due east. (a) How far and {b} in what direction (south of due west} must he now travel to reach base camp? (3) Number n Units v (b) Number n Units v Current Attempt in Progress Here are three vectors in meters: d1 = -5.407 + 2.60 j + 8.20k d2 = - 2.007 - 4.00 ] + 2.00k d 3 = 2.007 + 3.00 7 + 1.00k What results from (a) d 1 . (d2 + d3 ), (b) d1 - (d2 x d3 ), and d | x (d2 + d3 ) ((c), (d) and (e) for i, ] and k components respectively)? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number UnitsCurrent Attempt in Progress i For the following three vectors, what is 2 - C . 3.001- + 3.00'} 3.001% 3 2.002- + 3.00\"} + 3.003 7.00? 8.00} ('31, cal, >1, || Number n Units If di + d2 = 5.0d3, di - d2 = 3.0d, and d 3 = 2.6i + 4.5 j, then what are (a) the x component of d1, (b) the y component of dj, (c) the x component of d2, and (d) the y component of d2? (a) Number i Units (b) Number Units (c) Number i Units (d) Number i UnitsIf B is added to C = 7.6i + 7.1 j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B? Number i UnitsTwo vectors are given by a = 1.li + 2.1j and b = 3.97 + 5.7). Find (a) | d x bl, (b) d . b. (c)( a + b ) . b, and (d) the component of a along the direction of b. (a) Number Units (b) Number Units (c) Number Units (d) Number UnitsWhat is the magnitude of a x ( b x a ) if there is an angle Q = 42.0 between the directions of a and b ? Assume a = 5.9 and b = 2.4. Number i UnitsOasis B is 8.0 km due east of oasis A. Starting from oasis A, a camel walls 23 km in a direction 15.0a south of east and then walks 32 km due north. if it is to then walk directly to B, (a) how far and (b) in what direction (relative to the positive x-axis within the range (-180, 180]) should it walk? (r!) (a) Number n Units v [b] Number n Units v A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: d | for 0.21 m southwest (that is, at 450 from directly south and from directly west), d 2 for 0.44 m due east, and d 3 for 0.72 m at 60 north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of d , ? What are (c) the x component and (d) the y component of d 2? What are (e) the x component and (f) the y component of d 3? What are (g) the x component and (h) the y component, (i) the magnitude, and (i) the direction of the ant's net displacement? If the ant is to return directly to the starting point, (k) how far and (I) in what direction should it move? Give all angles as positive (counterclockwise) angles relative to the +x-axis. (a) Number Units (b) Number i Units (c) Number i Units (d) Number Units{6) Number {fl Number {g} Number {h} Number {i} Number {1'} Number {k} Number (I) Number Units Units Units Units Units Units Units Units