Answer:
S = 49.25i + 113.04j with magnitude 123.22km
Explanation:
The net displacement has both x and y components.
S = S(x)i + S(y)j
The x component of the net displacement is given as the sum of the x component of the first and second displacements:
S(x) = S(1,x) + S(2,x)
S(1,x) = 50 cos(90)
S(1,x) = 0 km
S(2,x) = 80 sin (38)
S(2,x) = 49.25km
=> S(x) = 0 + 49.25
S(x) = 49.25km
The y component of the net displacement is given as the sum of the y component of the first and second displacements:
S(y) = S(1,y) + S(2,y)
S(1,y) = 50 sin(90)
S(1,y) = 50km
S(2,y) = 80 cos (38)
S(2,y) = 63.04 km
=> S(y) = 50 + 63.04
S(y) = 113.04 km
=> S = 49.25i + 113.04j
Hence, the magnitude of the net displacement will be
S = √(S(x)² + S(y)²)
S = √(49.25² + 113.04²)
S = √(15183.94)
S = 123.22km
