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Kinematics

Problem 1.35

1.34. A balloon starts rising from the surface of the Earth. The ascension rate is constant and equal to \(v_{0}\). Due to the wind the balloon gathers the horizontal velocity component \(v_{x}=a y,\) where \(a\) is a constant and \(y\) is the height of ascent. Find how the following quantities depend on the height of ascent: (a) the horizontal drift of the balloon \(x(y)\); (b) the total, tangential, and normal accelerations of the balloon.

Reveal Answer
 (a) y=(b/2a)x2; (b) R=v2/wn=v2/wˉ2−wτ2==(a/b)[1+(xb/a)2]3/2\text { (a) } \quad y=(b / 2 a) x^{2} ; \text { (b) } \quad R=v^{2} / w_{n}=v^{2} / \sqrt{\bar{w}^{2}-w_{\tau}^{2}}= =(a / b)\left[1+(x b / a)^{2}\right]^{3 / 2}
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