Luke is swimming in a river with a current flowing west to east at a constant speed of 3.5 meters/second. Assume that Luke's water speed is a constant 5 meters/second. If he tries to swim 60° east of north, his resultant speed is 2.63 6.58 7.40 8.22 8.52 meters/second and his direction angle is 17.70 35.82 71.63 103.01 144.18 °.

Question

Mathematics

Shayna Wang

2 December, 01:06

Luke is swimming in a river with a current flowing west to east at a constant speed of 3.5 meters/second. Assume that Luke's water speed is a constant 5 meters/second. If he tries to swim 60° east of north, his resultant speed is 2.63 6.58 7.40 8.22 8.52 meters/second and his direction angle is 17.70 35.82 71.63 103.01 144.18 °.

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Alma · Answer 1

Decompose each velocity in its i and j - coordinates.

1) River's velocity

3.5 m/s, west fo east = 3.5i + 0j

2) Luke's velocity

5m/s, 60° east of north

5 * sin (60°) i + 5*cos (60°) j = 4.33 i + 2.5 j

3) Resultant velocity

[3.5i + 0j] + [4.33i + 2.5j] = 7.83i + 2.5j

resultant speed = √[ (7.83) ^2 + (2.5) ^2 ] = 8.22 m/s

angle = arctan (2.5 / 7.83) = 17.7° north of east (equal to 72.3° east of north).