Two students, each riding bicycles, start from the same apartment building and r

Question

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. The first student rides 1300 m due east and then turns due north and travels another 1430 m before arriving at the destination. The second student heads due north for 1930 m and then turns and heads directly toward the destination.

(a) At the turning point, how far is the second student from the destination?

___________m

(b) During the last leg of the trip, what direction (measured relative to due east) must the second student head? (Give your answer as a positive number from 0 to 180 degrees, either north or south of due east.)

____° south of east

Explanation / Answer

here,

the destination , d = 1300 m i + 1430 m j

the seccond student displacement , d2 = 1930 m j + xi + y j

d1 = d2 (as the destination is same)

x = 1300 m , y = - 500 m

(a)

the distance of seccond student from the destination , r = sqrt(x^2 + y^2)

r = 1392.83 m

(c)

the direction is theta = arctan(-500/1300)

theta = 21.04 degree south of east

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