Question

a deer hunter moves 75 km horizontally, then travels 25 km at an angle of 35 degrees above horizontal to his deer stand. what is the displacement from his starting point?

Answer 1

The displacement from his starting point is approximately 76.89 km .

To find the displacement, you can use vector addition because the hunter's movement involves both horizontal and vertical components.

Horizontal Component:

The hunter moves 75 km horizontally, so the horizontal component is 75 km.

Vertical Component:

The hunter travels 25 km at an angle of 35 degrees above the horizontal. To find the vertical component, you can use trigonometry. The vertical component is given by:

Vertical Component=Horizontal Distance × tan(Angle)

Vertical Component=25×tan(35 ∘ )

Vertical Component≈25×0.700

Vertical Component≈17.50

Displacement:

The displacement is the vector sum of the horizontal and vertical components. You can use the Pythagorean theorem:

Displacement=
`\sqrt{(Horizontal Component)^(2) +(Vertical Component) ^(2) }`

Displacement=
`\sqrt{75^(2) + 17.50 ^(2) }`

Displacement=
`√(5625+306.25 )`

Displacement ≈
`√(5931.25 )`

Displacement ≈ 76.89km.