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Unformatted text preview: Solutions to Homework #2 Chapter 3 12. Picture the Problem : The four possible locations of the treasure are labeled A , B , C , and D in the figure at right. The position vector for location A is also drawn. North is up and east is to the right. Strategy: Use the vector components to find the magnitude and direction of each vector. Solution: 1. Find the magnitude of A r : ( 29 ( 29 2 2 25.0 m 12.0 5.00 m 30.2 m A = + + = 2. Find the direction from north of A r : 1 25.0 m tan 55.8 west of north 12.0 5.00 m A θ = = ° ÷ + 3. Find the magnitude of B r : ( 29 ( 29 2 2 25.0 m 12.0 5.00 m 26.0 m B = + = 4. Find the direction from north of B r : 1 25.0 m tan 74.4 west of north 12.0 5.00 m B θ = = ° ÷ 5. Find the magnitude of C r : ( 29 ( 29 2 2 25.0 m 12.0 5.00 m 30.2 m C = + + = 6. Find the direction from north of C r : 1 25.0 m tan 55.8 east of north 12.0 5.00 m C θ = = ° ÷ + 7. Find the magnitude of D r : ( 29 ( 29 2 2 25.0 m 12.0 5.00 m 26.0 m D = + = 8. Find the direction from north of D r : 1 25.0 m tan 74.4 east of north 12.0 5.00 m D θ = = ° ÷ Insight: If you ever find a treasure map like this one, you’ll be glad you mastered vectors in physics! 18. Picture the Problem : The vectors involved in the problem are depicted at right. Strategy: Since A r points entirely in the x direction, and B r points entirely in the y direction, A r and B r are the x and y components of their sum + A B r r . Use the known lengths of + A B r r and A r to find B . Solution: 1. Set the length of + A B r r equal to 37 units: 2. Solve for B : Insight: Here the length of B r is determined by the lengths of the other two vectors because the directions of A r and B r are stipulated. Learning to manipulate vector components will be a useful skill when tackling many physics problems. 12.0 m 25.0 m 25.0 m 5.00 m A B C D palm tree A r θ A x y B r A r + A B r r −22 O 30 26. Picture the Problem : The vectors involved in the problem are depicted at right....
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 Fall '08
 Ashkenkai
 Physics, Acceleration, Work, Velocity, 2 g, 15°, 26.0 m

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