The coordinates of a particle moving in a plane are given by x = 4 cos 6t and y = 6 sin 6t (a) find the equation of the path of the particle
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- A woman walks 171 m in the direction 32° east of north, then 161 m directly east. Find (a) the magnitude and (b) the angle (from due east) of her final displacement from the starting point. (c) Find the distance she walks.Given three vectors A = 24i + 33j, B = 55i - 12j and C = 2i + 43j (a) Find the magnitude of each vectorDetermine the vector magnitudes and directions for the relative velocities VA/B and VB/A, given these magnitudes and directions for the vectors VA and VB:(a) VA: magnitude 70km/h ; direction 30°VB: magnitude 50km/h ; direction 125° (b)VA: magnitude 70km/h ; direction 30°VB: magnitude 50km/h ; direction 225° (c) VA: magnitude 70km/h ; direction 30°VB: magnitude 50km/h ; direction 340° (d)VA: magnitude 70km/h ; direction 135°VB: magnitude 50km/h ; direction 60°NOTE: The direction is the angle (degrees) from the positive horizontal axes in an anticlockwise direction.
- (a) You are standing on one side of a river and a tree is directly across from you. You then walk adistance d along the river and determine that now the tree is at an angle θ. How wide is the river?A plane travels north at speed v0 for a time t0 and then travels east at 12v0 for a time 3t0. (b) How farto the north did the plane travel? How far to the east? (c) What is the total distance the plane is awayfrom its initial position?The position vector r describes the path of an object moving in space. Find the velocity v (t), speeds (t), and acceleration a (t), of the object. r(t) = (et cos(t), et sin(t), et) v(t) = +These are the component forms of vectors u and w: ū u = (-4,-3) w = (–1,5) Add the vectors. u+w=