HW 4 - Math E-21a Fall 2009 HW #4 problems Problems to turn...

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Math E-21a – Fall 2009 – HW #4 problems Problems to turn in on Thurs, Oct 1: Note: Bold indicates vector quantities. Section 10.2 : 38. Prove formula 3 of Theorem 3:  () () d f tt f f t t dt  uu u where () f t is s scalar-valued function and t u is a vector-valued function. 46. If a curve in R 3 has the property that the position vector ( ) t r is always perpendicular to the tangent vector t r , show that the curve lies on a sphere with center at the origin. Section 10.3 : 2. Find the length of the curve 2 ,s in cos,cos s in , 0 t t t t t  r . 4. Find the length of the curve 3 2 2 () 12 8 3 , 0 1 t t t ri j k . Section 10.4 : 8. Find the velocity, acceleration, and speed of a particle with the given position function. Sketch the path of the particle and draw the velocity and acceleration vectors for the specified value of t : 2cos s in , 0 t t t  jk 12. Find the velocity, acceleration, and speed of a particle with the given position function: 2 s cos tttt j k 34. Find the tangential and normal components of the acceleration vector for the curve described by 2 3 ttt t   j k . [Note : These components (scalar projections) will be functions of t .] Section 10.5 :
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HW 4 - Math E-21a Fall 2009 HW #4 problems Problems to turn...

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