A man cycles 5 miles due north and 12 miles due east.
a. what is the distance traveled by the man?
b. what is displacement of the man?
man rides 5+12 = 17 mi
displacement = √(25+144) = 13 mi
To answer these questions, we can use the Pythagorean theorem to find the distance traveled and trigonometry to find the displacement.
a. Distance Traveled:
The distance traveled is the total length covered by the man on his bike. We can calculate this by finding the hypotenuse of a right triangle formed by the vertical (north) and horizontal (east) legs.
Using the Pythagorean theorem:
Distance = √(5² + 12²)
= √(25 + 144)
= √169
= 13 miles
Therefore, the man has traveled a distance of 13 miles.
b. Displacement:
The displacement is the shortest straight-line distance from the initial point to the final point. We can calculate this using trigonometry.
Since the man cycled 5 miles north and 12 miles east, we can change this information into a right triangle. The distance north can be considered the opposite side (O) and the distance east can be considered the adjacent side (A) of this right triangle.
The displacement, D, can be found using the formula:
D = √(O² + A²)
= √(5² + 12²)
= √(25 + 144)
= √169
= 13 miles
Therefore, the displacement of the man is also 13 miles.