Question

The emperor penguin is the best diver among birds: the record dive is 483 m. Suppose an emperor penguin dives vertically to a depth of 483 m and then swims horizontally a distance of 225 m. What angle would the vector of the resultant displacement make with the water's surface? What is the magnitude of the penguin's resultant displacement?

Answer 1

To determine the angle, use arctan(225/483). For the magnitude of the resultant displacement, calculate the square root of the sum of the squares of the vertical and horizontal distances.

Step-by-step explanation:

Determining the Resultant Displacement and Angle

To solve for the angle that the vector of the resultant displacement makes with the water's surface, we need to treat the problem as a right triangle with sides of 483 m (vertical dive) and 225 m (horizontal swim). The resultant displacement is the hypotenuse of this triangle.

To find the angle with the water's surface, we can use the arctan function which is the inverse of the tangent function in trigonometry. This angle will be arctan(225/483).

To find the magnitude of the resultant displacement, we can use the Pythagorean theorem:

Resultant Displacement = √(vertical distance² + horizontal distance²)

Plug in the values:

Resultant Displacement = √(483 m² + 225 m²)

This will give us the magnitude of the displacement.