Question

g The ant has traveled 10 cm horizontally and 6 cm vertically from its starting point on a twig with a slope of 0.5. If this is the only information the ant has, what function best approximates the geometry of the twig at the point the ant is on? b) The ant can use its model of the environment to plan its movements. In particular, it wants its next step to take it no higher than 0.1 cm above its current location. How far can the ant travel horizontally and still accomplish this?

Answer 1

Answer:

a)  a right triangle,  b)   x = 0.167 m

Explanation:

a) It is asked to find which geometry figure describes the movement of the ant.

Let's use trigonometry with the angles measured in radians

             tan θ = y / x

             tan θ = 6/10  

             θ = tan⁻¹ 0.6

             θ = 0.54 rad

this value is equal to the upward slope therefore the geometric body that describes the movement is a right triangle

b) it is asked to find the horizontal displacement for a vertical displacement of y = 0.1 cm x = y / tan tea

            x = 0.1 / tan 0.54

            x = 0.1668 m

            x = 0.167 m