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Unformatted text preview: Chapter 4 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 4.1 The Position, Velocity, and Acceleration Vectors 1. A motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00-min trip, find (a) the total vector displacement, (b) the average speed, and (c) the average velocity. Let the positive x axis point east. 2. A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions: x = (18.0 m/s) t and y = (4.00 m/s) t (4.90 m/s 2 ) t 2 (a) Write a vector expression for the balls position as a function of time, using the unit vectors i and j . By taking derivatives, obtain expressions for (b) the velocity vector v as a function of time and (c) the acceleration vector a as a function of time. Next use unit-vector notation to write expressions for (d) the position, (e) the velocity, and (f) the acceleration of the golf ball, all at t = 3.00 s. 3. When the Sun is directly overhead, a hawk dives toward the ground with a constant velocity of 5.00 m/s at 60.0 below the horizontal. Calculate the speed of her shadow on the level ground. 4. The coordinates of an object moving in the xy plane vary with time according to the equations x = (5.00 m) sin( wt ) and y = (4.00 m) (5.00 m)cos( wt ), where w is a constant and t is in seconds. (a) Determine the components of velocity and components of acceleration at t = 0. (b) Write expressions for the position vector, the velocity vector, and the acceleration vector at any time t > 0. (c) Describe the path of the object in an xy plot. Section 4.2 Two-Dimensional Motion with Constant Acceleration 5. At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of v i = 3.00 i - 2.00 j ( 29 m / s and is at the origin. At t = 3.00 s, the particle's velocity is v = 9.00 i + 7.00 j ( 29 m / s . Find (a) the acceleration of the particle and (b) its coordinates at any time t . 6. The vector position of a particle varies in time according to the expression r = 3.00 i - 6.00 t 2 j ( 29 m . (a) Find expressions for the velocity and acceleration as functions of time. (b) Determine the particle's position and velocity at t = 1.00 s....
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