# hw1 - Homework No 1 Vector components CHANG 1 A boat is...

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Homework No. 1 O a = 5 m/s 2 υ = 20 m/s x 1 y 1 x 2 y 2 50° 30° 20° Vector components CHANG 1 A boat is traveling along a curved path, and when it reaches point O the acceleration of the boat a and the velocity of the wind G υ G are shown in the figure. Find the components of both vectors with respect to x 1 - y 1 as well as x 2 - y 2 coordinate systems. Ans : a x 1 = 2.5 m/s 2 , a y 1 = 4.33 m/s 2 ; a x 2 = 3.83 m/s 2 , a y 2 = 3.21 m/s 2 ; υ x 1 = 15.3 m/s, υ y 1 = 12.9 m/s; υ x 2 = 10 m/s, υ y 2 = 17.3 m/s O A = 500 N B = 200 N x 1 y 1 x 2 y 2 75° 35° 25° CHANG 2 Two tug boats A and B guiding a ship at point O exert forces on the ship shown in the figure. Find the components of both force vectors with respect to x 1 - y 1 as well as x 2 - y 2 coordinate systems. Ans : A x 1 = 211 N, A y 1 = 453 N; A x 2 = 433 N, A y 2 = 250 N; B B x 1 = 51.8 N, B y 1 B = 193 N; B B x 2 = 68.4 N, B y 2 B = 188 N Y&F 1.40 Ans : (a) 10.0 cm, 149 ° (b) 10.0 m, 166 ° (or 194 ° ) (c) 8.21 km, 19.2 ° (or 341 ° ) Vector addition by the components method

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• Spring '08
• TSChang

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