Question

A hot-air balloon is rising vertically at a rate of 70 feet per second

and the wind is blowing due East at a rate of 30 feet per second.
(a) Determine the resultant vector v, representing the actual path of the balloon
as a result of combining the upward force and the wind.
(c) Determine the speed of the balloon along its path. Round to the tenths place .

Answer 1

(a)
`\mathbf{\vec{v}}` = 30·i + 70·j

(b) The direction is 66.8° North of East

(b) The speed of the balloon is 76.2 ft/s

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
`\mathbf{\vec{v}}` = 30·i + 70·j

(b) The direction is given by
`tan^(-1)(Vertical \ component)/(Horizontal \ component) = tan^(-1) (70)/(30) = 66.8014 ^(\circ)`

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.