Question

2.

General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s (2i +3j +5k)m,s2 (6i-91+ 2krn, and s,-(10i + 8j-km a) Find the resultant displacement in terms of unit vectors and components. b) State the magnitude of the resultant displacement. 2. Suppose a hiker travels 5 km southwest from their camp. Then, the hiker travels 2 km 75° north of east. a) Find the displacement of the hiker form their camp. b) If the hiker then travels another 3 km south of west, what then is the hiker's displacement. c) Express the hiker's displacement in a) and b) in terms of unit vectors. A robot moves within a grid along two coordinate axes such that its position in meters as a function of time is given by: x(t)--3t2 +4t 1 and y(t) t2 5t +6 a) What is the robot's position vector in unit vector notation at t-10 s? b) What is the robot's velocity at t-10 s? 4. At the beginning of a 3.0 hr plane trip, you are travelling due north at 192 km/hr. At the end you are travelling 240 km/hr in a northwest direction. a) Find your change in velocity b) Find your average acceleration during this 3.0 hr trip. 2D Kinematics/Motion with Constant Acceleration 5. A particle moves with an initial velocity x-component of 12 m/s and a y-component of -4 m/s from an origin at time, t-0. The particle moves in the x-y plane with an x component of acceleration given by a 3.0m/s2 a) Express the components of the velocity vector at any given time. b) Find the total velocity vector at any given time. c) Calculate the velocity and speed of the particle at t-5 s. 6. What are the kinematic equations used for x and y components for motion in a plane (2D)? 7. Projectile Motion Example 1. A ball is launched at an angle of 30 degrees wir to the ground with a velocity of 15 m/s. Neglecting air resistance and no horizontal change in motion, answer and do the following: a) While the ball is in motion what does the vertical and horizontal component of acceleration do? Increase, decrease, or remain constant? b) Is there any component of velocity that is zero at any point in its motion? Is there any component of acceleration equal to zero at any point in its motion? c) Describe the speed of the ball during its entire path. Also, do a vector sketch of the velocity of the ball during its entire path showing component vectors, d) What is the maximum height that can be reached by the ball?

Answer 1