Homework Solutions 7 - homework 03 ASH, BEN Due: Feb 6...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: homework 03 ASH, BEN Due: Feb 6 2008, 11:00 pm 1 Question 1, chap 3, sect 99. part 1 of 2 10 points A ship cruises forward at v s = 6 m / s rel- ative to the water. On deck, a man walks diagonally toward the bow such that his path forms an angle = 19 with a line perpen- dicular to the boats direction of motion. He walks at v m = 2 m / s relative to the boat. Draw the vectors to scale on a graph to determine the answer. v s v m At what speed does he walk relative to the water? Correct answer: 6 . 91474 m / s (tolerance 5 %). Explanation: v s v v m Scale: 1 m Let : v s = 6 m / s v m = 2 m / s v = 6 . 91474 m / s = 71 = 55 . 1286 = 161 , and = 15 . 8714 . When you complete the parallelogram, the resultant velocity v with respect to the water is the side of the triangle opposite the obtuse angle, which has a measure of = 90 + . Let vectorv s be the velocity of the ship, vectorv m be the velocity of the man, and vectorv be the resultant velocity of the man relative to the water (Earth). By the law of cosines v 2 = v 2 m + v 2 s 2 v m v s cos v = bracketleftbig v 2 m + v 2 s 2 v m v s cos bracketrightbig 1 / 2 = bracketleftbig (2 m / s) 2 + (6 m / s) 2 2(2 m / s)(6 m / s) cos(109 )] 1 / 2 = bracketleftbig (2 m / s) 2 + (6 m / s) 2 +(7 . 81363 m 2 / s 2 ) bracketrightbig 1 / 2 = 6 . 91474 m / s . Alternatively: We can analyze the vector addition using the components of the vectors. Note: vectorv = vectorv s + vectorv m , or v x = v s + v m sin = (6 m / s) + (2 m / s) sin(19 ) = 6 . 65114 m / s and v y = v m cos = (2 m / s) cos(19 ) = 1 . 89104 m / s Hence the speed of the man with respect to the water is v = radicalBig v 2 x + v 2 y = radicalBig (6 . 65114 m / s) 2 + (1 . 89104 m / s) 2 = 6 . 91474 m / s . Question 2, chap 3, sect 99. part 2 of 2 10 points At what angle to his intended path does the man walk with respect to the water? Correct answer: 55 . 1286 (tolerance 5 %). Explanation: The law of sines can be used to compute the requested angle , which is the angle opposite the ships path and velocity. sin v s = sin v homework 03 ASH, BEN Due: Feb 6 2008, 11:00 pm 2 sin = v s v sin = arcsin bracketleftBig v s v sin bracketrightBig = arcsin bracketleftbigg 6 m / s 6 . 91474 m / s sin(109 ) bracketrightbigg = 55 . 1286 . Alternate Solution: Using vector compo- nents from Part 1, we have tan = v y v x = arctan parenleftbigg v y v x parenrightbigg = arctan parenleftbigg 1 . 89104 m / s 6 . 65114 m / s parenrightbigg = 15 . 8714 . Therefore the angle between vectorv m and vectorv is = 90 = 90 (19 ) (15 . 8714 ) = 55 . 1286 ....
View Full Document

This note was uploaded on 09/29/2008 for the course PHY 303 taught by Professor Erskine/tsoi during the Spring '08 term at University of Texas at Austin.

Page1 / 12

Homework Solutions 7 - homework 03 ASH, BEN Due: Feb 6...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online