A man leaves his front door, walks 1000 ft east, 2000 ft north, and then takes a penny from his pocket and drops it from a cliff 500 ft Set up a coordinate system and write down an expression, using unit vectors, for the displacement of the The man then returns to his front door, following a different path on the return trip. What is his resultant displacement for the round trip?

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 101 m at an angle 30.0° north of east, and finally moves 184 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 S E Final position What is the resultant displacement from the entrance? magnitude direction m ° south of east

A vector has the components Ax=22mAx=22m and Ay=16mAy=16m. a) What is the magnitude of this vector? Express your answer to two significant figures and include appropriate units.   b) What angle does this vector make with the positive x axis? Express your answer to two significant figures and include appropriate units.

Vector A= -6i+4j Vector B= -3i-8j How do you find the quantity of abs(A+B)?

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 115 m at an angle 30.0° north of east, and 185 m south. Find the resultant displacement from the cave entrance. The figure below suggests the situation but is not drawn to scale.

A girl delivering newspapers covers her route by traveling 5.00 blocks west, 4.00 blocks north, and then 4.00 blocks east. (a) What is her resultant displacement? Your response differs from the correct answer by more than 10%. Double check your calculations. blocks

Margaret walks into the store using the following path: 0.870 mi west, 0.330 mi north, 0.140 mi east. Assume north be along the positive y axis and west be along the negative x axis. What is the magnitude of her total displacement? In what direction is the displacement vector? Enter the answer as an angle north of west.

The vector A has a magnitude of 4.0 meters and points in the -x direction. The vector B has a magnitude of 3.0 meters and points in the +y direction. Vector C is defined so that C - A + B = 0. What is the magnitude and direction of vector C? Give your answers to 2 significant figures.

Let C = A + B. Vector C has a length of 5.00 cm and points north. Vector A has length 2.30 cm and a direction of 58.0 degrees north of east. (Let north = +y and east= +x).a) Draw a vector addition diagram showing C = A + B and label all 3 vectors. Use a straight edge and draw them to scale in cm if possible (you can estimate the angle).b) What is the magnitude of vector B? c) What is the angle of B in degrees west of north? d) Let D = C x A (vector product of C and A). What is the magnitude and direction of vector D?e) What angle (in degrees) does vector E= 2.00i+ 4.00j-3.00k make with the +y axis?

If you want to go by train from Los Angeles to New York, you must make a stop. First, you musttravel 1800 miles East to reach New Orleans. Then you must travel 1300 miles at 45◦ North of Eastto reach New York.(a) Graph the vectors for each segment of the trip and the resulting displacement. Each tick markshould represent 300 miles.(b) If you flew directly from Los Angeles to New York, how far would the flight be? Please show your work