A room has dimensions 2.44 m (height) × 5.76 m × 6.24 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) If the fly walks rather than flies, what is the length of the shortest path it can take? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)

one day you go hiking at a nearby nature preserve. at first, you follow the straight, clearly marked trails. from your starting point, you travel 2.00 miles down the 1st trail. then you turn to your left by 30.0 degrees to follow a 2nd trail for 1.40 miles. next, you turn to your right by 160 degrees and follow a third trail for 1.90 miles. at this point you are getting very tired and would like to go back.   you would like to take a shortcut directly through the woods. how far to your right should you turn, and how far do you have to walk, to go directly back to the darting point.       what degree turn to the right must "I" take, and how many miles must I walk back?       I know the distance is 2.104 miles, but I cannot figure out the degree angle.

Vector A = 53.0 cm is at an angle of 270° from the horizontal, and vector B = 82.0 cm is at angle 0. (a) What is |A + BỊ (in cm) as a function of 0? (Use the following as necessary: 0. Do not include units in your answer.) JA + B| = cm (b) Using the result from part (a), for what value of e (in degrees) does |A + B| take on its maximum value? What is this maximum value (in cm)? cm (c) Using the result from part (a), for what value of e (in degrees) does |A + B| take on its minimum value? What is this minimum value (in cm)? cm (d) What If? How would your answers to parts (a)-(c) change if B was now subtracted from A and the magnitude of A - B| was evaluated as a function of 0? (Enter the magnitude as a function of e in cm. Do not include units in your answer. Enter the maximum and minimum values in cm.) A - B = cm Maximum value cm Minimum value cm

one afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 2.56 km. They start at the west side of the lake and head due south to begin with. (a) what is the distance they travel? (b) the magnitude of the couple's displacement? (c) what is the direction(relative to due east) of the couple's displacement?

Vector A lies in quadrant 2 of the xy-plane. Vector B lies in quadrant 1 of the xy-plane. In what direction does the vector A x B point? K, -k, j or -j And why?

Vector Ä has a magnitude of 10 units and a direction angle of 14° measured counterclockwise from the positive r-axis. Vector B has the same r-component as Ä, but its y-component is 3 times larger. What is the magnitude and direction angle of vector B?

Find the magnitude of the vector v = 9 cos(90)i + 9 sin(90) j. (Give an exact answer. Use symbolic notation and fractions where needed.) ||v|| =

A room has dimensions 2.71 m (height) × 4.05 m × 6.99 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) If the fly walks rather than flies, what is the length of the shortest path it can take? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)

The three vectors in the figure have magnitudes a = 3.20 m, b = 3.20 m, and c = 10.2 m and angle e = 43.0°. What are (a) the x component and (b) the y component of á ; (c) the x component and (d) the y component of b; and (e) the x component and (f) the y component of ? If 7 = pd + qb, what are the values of (g) p and (h) q? (a) Number Units (b) Number Units (c) Number |Units (d) Number Units (e) Number Units (f) Number |Units (g) Number Units (h) Number Units

A sailboat race course consists of four legs, defined by the displacement vectors A, B, C, and, as the drawing indicates. The magnitudes of the first three vectors are A = 2.90 km, B = 4.90 km, and C= 5.30 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find (a) the distance of the fourth leg and (b) the angle (. (a) Number i 6.67 (b) Number 21.29 Units Units 0 0 23.0 7 B km + Finish- B 35.0 X 40.0° Start