The car, moving in a straight line, drove a path of 10 meters, then made a turn, circumscribing a quarter
The car, moving in a straight line, drove a path of 10 meters, then made a turn, circumscribing a quarter circle with a radius of 10 meters, and drove further along a straight line for 10 meters. Determine the path traveled by him and the module of movement.
S1 = 10 m.
n = 1/4.
R = 10 m.
S2 = 10 m.
L -?
S -?
By the movement of the body L is called the length of the line that the body describes during movement. When moving, the body passed two straight sections with a length of S1 = 10 m, S2 = 10 m and 1/4 of the circumference of a circle with a radius R.
L = S1 + S2 + n * 2 * P * R.
L = 10 m + 10 m + 2 * 3.14 * 10 m / 4 = 35.7 m.
The movement of the body S is a vector that connects the initial and final position of the body. The movement of the car S will be the hypotenuse of a right-angled triangle with legs S1 + R and S2 + R.
By the Pythagorean theorem: S = √ ((S1 + R) ^ 2 + (S2 + R) ^ 2).
S = √ ((10m + 10m) ^ 2 + (10m + 10m) ^ 2) = 28.28m.
Answer: vehicle path L = 35.7 m, displacement S = 28.28 m.