A student decides to spend spring break by driving 50 miles due east, then 50 miles 30 degrees south of east, then 50 miles 30 degrees south of that direction, and to continue to drive 50 miles deviating by 30 degrees each time until he returns to his original position. How far will he drive, and how many vectors must he sum to calculate his displacement

Explanation: The movement described in the question exhibits that of a polygon. Exhibiting a constant distance and angle with only varying direction until the starting point is reached.

The sum of exterior angles of a polygon = 360 degrees.

Exterior angle of a polygon = (360 ÷ number of sides)

Therefore,

Number of sides = 360 ÷ exterior angle

Exterior angle = 30 degrees

Hence,

Number of sides = 360 ÷ 30 = 12 sides

Since distance traveled of 50 miles is the same for each displacement ;

Total displacement = distance traveled * number of sides

Total displacement = 50 * 12 = 600 miles.

ConcepcionPetillo ConcepcionPetillo · Answer 2 · 2022-03-25T13:46:28+01:00

He drives 600 miles and he has to sum a total of 12 vectors to calculate the distance.

Calculating the total distance:

According to the question, the motion represents a polygon.

The sum of all exterior angles of a polygon = 360 degrees.

Thus,

Number of sides = 360 ÷ exterior angle

Given that the exterior angle = 30°

Therefore:

Number of sides = 360 ÷ 30 = 12 sides

Now.

Total distance = distance traveled × number of sides

Given that the distance traveled = 50 miles

Total distance = 50 × 12 = 600 miles.

The total displacement will be 0 since he returns to his original position.

Learn more about polygons:

https://brainly.com/question/17756657?referrer=searchResults