P2F10-Tut6-soln - P2 Tutorial #6 Dot Products: Relative...

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P2 Tutorial #6 Relative Velocity and Dot (Scalar) Product 11/3/2010 Dot Products: 1. (a) In general, vectors can be write down in two different forms, i.e. Cartesian : ⃗± ² (³ ´ µ ³ ) or Polar form : ⃗± ² ·³µ ¸¹ , where A is the magnitude of the vector. What are two different ways of computing the dot (or scalar) product between two vectors, ⃗± º » ⃗± ? (b) If you are given two vectors in polar form, which one of the way of would be easier to compute the dot product between them? Explain why. (c) Using your answer in part (a), explain what is wrong with computing ⃗± º (» ⃗± º ¼ ⃗± ) ? 2. Given ⃗± ² ½ ¾¿√À Á µ ¾ Á  and » ⃗± ² ·Ãµ ÄÅ Æ ¹ , where only » ⃗± is in the polar from and the angle is measured from the positive x-axis. (a) Draw a relevant vector diagram. (b) What is the component of » ⃗± along the direction of ⃗± ? How is this related to the dot product? (c) What is the component of ⃗± along the direction of Ç ⃗± ? 3. Find the dot product and the angle between the vectors. a. ⃗± ² ·Èµ ÃÉ Ê ¹ and » ⃗± ² ·Äµ ËËÌ ¾ ¹ , where both vectors are in polar form and each angles is measured from the positive x-axis. Note that the angle of » ⃗± is in radian. b. ¼ ⃗± ² ·Íµ ȹ and Î ⃗± ² ·Ïõ Ĺ c. Ð ⃗± ² ⃗± Ñ » ⃗± and Ò ⃗± ² ¼ ⃗± Ñ Î ⃗± d. Ó ⃗± ² ·Ãµ ȹ and Ô ⃗⃗± ² ·Èµ Ïù e. Õ ± ² ·Ãµ Ĺ and Ö ± ² ·×µ ع f. Ù ⃗± ² ·Ãµ ȵ ȹ and Ú ⃗± ² ·Èµ Ïõ ͹ . In this case the vectors are 3D-vectors, (x,y,z) Relative Velocity: Solve following problems using the notation for relative motion as discussed in the lecture. Ex) Û ⃗± ÜÝ means the velocity of object A measured by observer B. 4.
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This note was uploaded on 11/21/2010 for the course PHYSICS Physics 2 taught by Professor Manojkaplinghat during the Fall '10 term at UC Irvine.

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P2F10-Tut6-soln - P2 Tutorial #6 Dot Products: Relative...

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