Question

A bat navigates 1.5 m west and 6.0 m north. Which of the following correctly describes the magnitude and direction of the bat's displacement with respect to its original position?

A. 38.3 m at 14°
B. 7.5 m at 19°
C. 4.5 m at 72°
D. 6.2 m at 76°

Answer 1

The magnitude of the bat's displacement is 6.2 m, and it is directed at an angle of about 76° from the westward direction, making D. 6.2 m at 76° the correct answer.

Step-by-step explanation:

To determine the magnitude and direction of the bat's displacement, we should use the Pythagorean theorem and trigonometry. The bat's displacement can be viewed as the hypotenuse of a right triangle with sides of 1.5 m west and 6.0 m north. The magnitude is given by the formula √(1.5² + 6.0²), which equals √(2.25 + 36) = √38.25 = 6.18 m (rounded to 6.2 m). To find the direction, we can use the tangent function, tan⁻¹(6.0/1.5), which gives us the angle relative to the westward direction. This angle is approximately 76°. Therefore, the correct answer that describes the magnitude and direction of the bat's displacement is D. 6.2 m at 76°.