A stone with weight w is thrown vertically upward into the air from ground level with initial speed v0. If a constant force f due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is

Question

A stone with weight w is thrown vertically upward into the air from ground level with initial speed v0. If a constant force f due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is (A) h=(v02/2 g(1+(f)w)) (B) h=(v02/2 g(1-(f)w)) (C) h=(v02/ g(1-(w)f)) (D) h=(v02/2 g(1-(w)f))

Tardigrade Admin · Accepted Answer

Using work energy theorem Wf+Wg=Δ K -f . h-W h=0-(1/2) m v02 h=(v02/2 g(1+(f)w))

Q. A stone with weight $w$ is thrown vertically upward into the air from ground level with initial speed $v_{0}$ . If a constant force $f$ due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is

$h = \frac{v _{0}^{2}}{2 g ( 1 + \frac{f}{w} )}$

$h = \frac{v _{0}^{2}}{2 g ( 1 - \frac{f}{w} )}$

$h = \frac{v _{0}^{2}}{g ( 1 - \frac{w}{f} )}$

$h = \frac{v _{0}^{2}}{2 g ( 1 - \frac{w}{f} )}$

Using work energy theorem
$W_{f} + W_{g} = Δ K$
$- f . h - Wh = 0 - \frac{1}{2} m v_{0}^{2}$
$h = \frac{v _{0}^{2}}{2 g ( 1 + \frac{f}{w} )}$

Q. A stone with weight w is thrown vertically upward into the air from ground level with initial speed v0​. If a constant force f due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is

h=2g(1+wf​)v02​​

h=2g(1−wf​)v02​​

h=g(1−fw​)v02​​

h=2g(1−fw​)v02​​