Jungle gym, dot products, unit vectors. A coordinate system is laid out along the bars of a large 3D jungle gym (the figure below). You start at the origin and then move according to the following steps. For each step, the distance (in meters) and direction in which you move are given by the cross product A x B of the given vectors A and B. For example, the first move is 18 m in the +z direction. What is the magnitude dnet of your final displacement from the origin? (a) A = 3.01, B = 6.0 (b) A = -4.01, B = 3.0k - − 8.0 (c) A = 2.0j, B = 4.0k (d) A = 3.0ĵ, B = (e) A = 4.0k, B = (f) A = 2.0î, B = - 2.01 − 4.0ĵ - #

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 247 m, and the car completes the turn in 33.0 s. Need the answer for C in degree format not coordinates  An x y coordinate axis is shown. Point A is located at a negative value on the y-axis, and an arrow points from point A to the right. A dotted line curves up and to the right in a quarter circle until it reaches point C on the positive x-axis. An arrow points directly upward from point C. Point B is on the dotted circle. A line drawn from the origin to point B makes an angle of 35.0° below the x-axis.   (a) Determine the car's speed. ___________ (b) What is the magnitude and direction of the acceleration when the car is at point B? magnitude       ___________ m/s2 direction _______________  ° counterclockwise from the +x-axis

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.

Bruce begins 7 kilometers to the north of town and rides his bike along a straight trail which leads to a park 3km west of town. It takes him 20 minutes to cover this distance. Write a vector in component form that describes his ride while also finding the magnitude and direction of this vector. Also, find the component of Bruce's motion which is in the direction of SW using a unit vector that uses both forms of the dot product (algebraic and geometric), then write parametric equations expressing his motion with the town being represented by the origin and t=0 being his starting point. Using these equations, what is his position after 5 minutes? Then eliminate the parameter to get a rectangular equation for this linear path and verify algabraically amd graphically that this equation represents the line.