Horizontal component:
x(t) = 5t + 6t²
x(5) = 25 + 6(25) = 175 m
Vertical component:
y(t) = 7 - 3t³
y(5) = 7 - 3(125) = -368 m
Components combined:
r(5) = (175 m) i - (368 m) j
Taken relative to the point r(0) = (0 i + 7 j) m ,
the displacement vector when t=5 is
(175 m) i - (375 m) j .
Its magnitude is √(175² + 375²)
= √(30,625 + 140,625)
= √171,250 = 413.823... m (rounded)
Its direction is tan⁻¹(-375/175) = tan⁻¹(-2.14285...) = - 64.98°
