Answer:
(a) [tex]\mathbf{\vec{v}}[/tex] = 30·i + 70·j
(b) The direction is 66.8° North of East
(b) The speed of the balloon is 76.2 ft/s
Step-by-step explanation:
(a) Here we have vertical component of velocity = 70 ft/s
Horizontal component of velocity = 30 ft/s
Therefore, the resultant vector representing the actual path of the balloon is [tex]\mathbf{\vec{v}}[/tex] = 30·i + 70·j
(b) The direction is given by [tex]tan^{-1}\frac{Vertical \ component}{Horizontal \ component} = tan^{-1} \frac{70}{30} = 66.8014 ^{\circ}[/tex]
Which is 66.8° North of East
(c) The speed of the hot air balloon is given by the magnitude of the resultant vector, v is given by v = √(70² + 30²) = 10√58 = 76.2 ft/s rounded to tenths.
