A straight river flows east at a speed of 12 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure). The motorboat has a speed of 22 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.) N 60° (a) Express the velocity of the river as a vector in component form. 12i

Let A= (3.0 m, 200south of east), B = (2.0 m, north), and C= (5.0 m, 700south of  west).  Draw and label A, B, and C with their tails at the origin. Use a coordinate system with the x-axis to the east.  b. Write A, B, and C in component form, using unit vectors.  c. Find the magnitude and the direction of D = A + B+ C.

F3 65° 35° F, The magnitude of the vector is F2=1.5N .What is the rectangular component of vector F2 ? * The magnitude of the vector is F2 = 1.5N. What is the rec tan gular component of vector F2? O (1.5N cos 65°) i + (1.5N cos 35°) j O (1.5N cos 35°) i + (1.5N cos 55°) j O (1.5 N) i + ( 1.5N ) j O (1.5N cos 55°) i + (1.5N cos 35°) j

Vector A measures 1.20m and angles 30° above the x-axis in the first quadrant. Vector B extends 3.20m and is angled 30° beneath the x-axis in the fourth quadrant. a. Determine the magnitude and direction of A + Bb. Determine the magnitude and direction of A – B

Problem 8: Consider two vectors A and B, expressed in unit vector notation as A= aji+ azj and B = bji+ bzj. A. Part (a) Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above. A+B = B 7 8 HOME a i j k 4 5 6 a1 a2 bị 1 2 3 b2 d + END - h VO BACKSPACE CLEAR m DEL Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. Part (b) Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above. Part (c) Enter an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions above.

Dr. B takes her dog ada on a walk. they start out heading south for 0.75 miles. then they turn left 30 degrees and they continue to walk for another 11 mile. Finally they turn right 9o degrees and they walk 1.9 miles. The whole walk takes 45 minutes.  What is the average speed of Dr.B and Ada on their walk? give your answer in m/s. What is the direction of the total displacement vector?

Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0 m north, then turns and moves 250 m east, then goes 113 m at an angle 30.0° north of east, and finally moves 179 m south. Find the resultant displacement from the cave entrance. Shown is a sketch of the situation not drawn to scale. (Give the magnitude of the displacement in m and the direction in degrees south of east.) Cave entrance W m N E o south of east 8 What is the resultant displacement from the entrance? magnitude direction Final position Q

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A flagpole sits at the center of a playground. Initially, a child is located 8.50 m due north of the flagpole. Two minutes later, the child is 6.00 m away from the flagpole in the direction 37.0° south of east. The displacement of the child lies between which two cardinal directions? O South and west O North and east O North and west O South and east

Two position vectors lie in a plane. The first, vector r points at an angle of 20° below the positive x-axis and has a magnitude of 57.5 m. The second, vector , points at an angle of 55.5° above the positive x-axis and has a magnitude of 75 m. (a) Choose the diagram below that is correct a graphical representation of + 78. +y +y magnitude direction FA FB fc 4 FA fc m FB Viewing Saved Mort: Be +X (counterclockwise from the +x-axis) +y +y FB FA ŤA fc fc (b) What is the magnitude and direction of vector re? Give the direction as an angle measured counterclockwise from the positive x- axis? FB +X + X Ad Tha