A group of tourists moved to the north for 20 km and then turning to the southeast

| April 9, 2021 | education

A group of tourists moved to the north for 20 km and then turning to the southeast passed another 40 km. define the path and movement.

S1 = 20 km.

S2 = 40 km.

L -?

S -?

The traversed path L is the length of the line that the body describes when moving. Since they first went through S1, and then another S2, the path traveled will be the sum: L = S1 + S2.

L = 20 km + 40 km = 60 km.

The displacement S is a vector that connects the starting and ending positions of the body.

Since the tourists walked to the north S1 = 20 km, and then to the southeast S2 = 40 km, the displacement S will be the length of the side of the triangle with sides S1 = 20 km and S2 = 40 km and the angle between them ∠α = 45 °.

By the cosine theorem, S = √ (S1 ^ 2 + S2 ^ 2 – 2 * S1 * S2 * cosα).

S = √ ((20 km) ^ 2 + (40 km) ^ 2 – 2 * 20 km * 40 km * cos45 °) = 29.7 km.

Answer: path L = 60 km, displacement S = 29.7 km.



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