Question

2 A sailboat on a lake sails 40. meters north and
then sails 40. meters due east. Compared to its
starting position, the new position of the sailboat
is
(1) 40. m due east (3) 57 m northeast
(2) 40. m due north (4) 80. m northeast

Answer 1

Answer: 3

57m north east

Explanation:

Given that the boat sails 40. meters north and then sails 40. meters due east. The new position will be known by using pythagorean theorem.

P^2 = 40^2 + 40^2

P^2 = 1600 + 1600

P^2 = 3200

P = square root (3200)

P = 56.6 m

P = 57 m (approximately )

Therefore, the new position of the sail boat will be 57 north east

Answer 2

Compared to its starting position, the new position of the sailboat is 57 m northeast

The given parameters;

initial displacement of the sail boat, x₁ = 40 m north

final displacement of the sail boat, x₂ = 40 m east

The new position of the sail boat when compared with the starting position is the total displacement of the sail boat.

A sketch of the sail boat displacement;

                                           ↑ →  →  →  →  →  → 40 m

                                           ↑

                                           ↑40 m

                                           ↑

The hypotenuse of this right triangle is the total displacement of the sail boat.

$R^2 = 40^2 + 40^2 \\\\R^2 = 3200\\\\R= \sqrt{3200} \\\\R = 56.57 \approx 57\ m$

The direction of the sail boat is northeast

Thus, compared to its starting position, the new position of the sailboat is 57 m northeast

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