Question

A kayaker paddles at 4.0 m/s in a direction 30° south of west. He then turns and paddles at 3.7 m/s in a direction 20° west of south.
What is the magnitude of the kayaker’s resultant velocity? Round your answer to the nearest tenth.

___m/s
What is the direction of the kayaker’s resultant velocity?

___ ° south of west
please help

Answer 1

7.2 m/s 

49 degrees south of west

Answer 2

Answer: The magnitude of the kayaker's resultant velocity = 7.23 m/s

and the direction is 49.26° south of west.

Explanation:

Initial velocity, u = 4.0 m/s 30° south of west.

Final velocity, v = 3.7 m/s 20° west of south °≈ 70° south of west.

Writing in terms of component:

u = -4.0 cos 30 i - 4.0 sin 30 j = -3.46 i -2.0 j

v = -3.7 cos 70 i - 3.7 sin 70 j = -1.26 i - 3.48 j

Resultant velocity = addition of the two velocity vectors

R = (-3.46 i -2.0 j)+(-1.26 i - 3.48 j) = -4.72 i - 5.48 j

Magnitude of the vector = √(-4.72)²+( - 5.48)² = 7.23 m/s

Direction of the resultant velocity vector, θ = tan⁻¹ (-5.48÷ (-4.72)) = 49.26° south of west.

Thus, the magnitude of the kayaker's resultant velocity = 7.23 m/s

and the direction is 49.26° south of west.