Question

a butterfly flies from the top of a tree in the center of a garden to rest on top of a red flower at the gardens edge. the tree is 9.0 m taller than the flower, and the garden is 17 m wide. part a determine the magnitude of the butterflys displacement. express your answer in meters.

Explanation:

Step1: Analyze horizontal displacement

The garden is 17 m wide. The butterfly moves from the center of the garden to the edge horizontally. The horizontal displacement $x=\frac{17}{2}= 8.5$ m.

Step2: Analyze vertical displacement

The tree is 9.0 m taller than the flower. So the vertical displacement $y = 9.0$ m.

Step3: Use Pythagorean theorem

The magnitude of the displacement $d$ of the butterfly is given by the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 8.5$ m and $y=9.0$ m into the formula: $d=\sqrt{(8.5)^{2}+(9.0)^{2}}=\sqrt{72.25 + 81}=\sqrt{153.25}\approx12.4$ m.

Answer:

12.4 m