Question

A ball is thrown vertically upward with speed u. If it experiences a constant air resistance force of magnitude f then the speed with which ball strikes the ground
Is​

Answer 1

$\huge \bold \green{Answer}$

according to the question

• A ball is thrown vertically upward with speed 'u'
• it experience a constant air resistance forc of magnitude 'f'
• let v be the speed with which ball strikes the ground (wt of ball is 'w' )
• let M donate the mass of the ball ( = w/g)

[g = gravitational acceleration]

• let H donate the maximum height reached by the ball

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$o = {u}^{2} - 2 \times (g + \frac{f}{m} ) \times h...(1a) \\ {v}^{2} = o + 2 \times (g - \frac{f}{m} ) \times ...(1b)$

From (1a) we get,

${u}^{2} = 2 \times( g + f \times \frac{g}{w} \times h[m = \frac{w}{g}] \\ or \: {u}^{2} = 2 \times g(f + w) \times \frac{h}{w} \\ or \: h = {u}^{2} \times \frac{w}{ 2 \times g[(f + w)] } ...(2a)$

From (1b) we get,

$\small {v}^{2} = o = 2 \times g(f - w) \times \frac{ {u}^{2} }{ [2 \times g(f + w)] }$

$or \: {v}^{2} = {u}^{2} \times \frac{ [(f - w) }{(f + w)] } \\ or \: v = u \times \frac{ \sqrt{[(f - w) } }{(f - w)]} ...(ans)$