A man is walking toward the back of an airplane at 7 m/s. The plane is flying West at 245 m/s. What is the speed and direction of the plane relative to the man?

The speed of the plane relative to the man is 245.1 m/s

The direction of the plane is S 88.36⁰ W

Explanation:

Given;

velocity of the man toward the airplane, Vy = 7 m/s

velocity of the airplane, Vx = 245 m/s west

The speed of the plane relative to man is given by;

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Complete this diagram to form a right angled triangle, with the hypotenuse as the relative velocity of the plan with respect to the man.

R² = 245² + 7²

R² = 60074

R = √60074

R = 245.1 m/s

The direction of the plane is given by;

tan θ = 245 / 7

tan θ = 35

θ = tan ⁻¹ (35)

θ = 88.36°

The direction of the plane is S 88.36⁰ W