Question

The friction of the air causes a vertical retardation equal to 10% of the acceleration equal to gravity .The maximum height will be decreased by how much percentage ?

Answer 1

Answer :

Given:

Friction due to air causes reduction in gravitational acceleration by 10%.

To find:

Maximum height reached will decrease by what percentage ?

Concept:

Air is a mixture of gases and hence acts like a fluid. Just like any liquid provides friction during flow , air also provides different kinds of frictional Force like Stroke's Force , Buoyancy Force , etc.

These cause the gravitational acceleration to decrease .

Calculation:

Let initial gravitational acceleration be g

New gravitational acceleration be g2

$g2 = g - 10\%(g)$

$= > g2 = g \times \dfrac{90}{100}$

$= > g2 = \dfrac{9g}{10}$

Initial maximum height be h , we know that :

${v}^{2} = {u}^{2} - 2gh$

$= > h = \dfrac{ {u}^{2} }{2g}$

Let new maximum height be h2 , we can say :

${v}^{2} = {u}^{2} - 2(g2)(h2)$

$= > h2 = \dfrac{ {u}^{2} }{2(g2)}$

$= > h2 = \dfrac{ {u}^{2} }{2 \times ( \frac{9g}{10} )}$

$= > h2 = \dfrac{5 {u}^{2} }{9g}$

Percentage change in height will be :

$=\dfrac{\dfrac{5u^2}{9g}\ -\ \dfrac{u^2}{2g}}{\dfrac{u^2}{2g}}\ \times\ 100\ \%$

$= \dfrac{( \dfrac{ 1}{18} )}{( \dfrac{1}{2} )} \times 100\%$

$= \dfrac{ 2}{18} \times 100\%$

$= 11.11 \: \%$

So final answer :

Percentage change in height is 11.11 %

Answer 2

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QUESTION :

The friction of the air causes a vertical retardation equal to 10% of the acceleration equal to gravity .

The maximum height will be decreased by how much percentage ?

SOLUTION :

From the question, we can see that :

The friction of the air causes a vertical retardation equal to 10% of the acceleration equal to gravity .

So, the actual g becomes 90% of g i.e , 9 / 10 g.

We know that :

V^2 - U^2 = - 2gH

V = 0

=> V^2 = 0

=> H = U^2 / 2g

New height :

H n = U^2 / 2 × { 9 / 10 g }

=> Hn = 5 U ^ 2 / 9 g

So, ∆ H = H - Hn

=> ∆ H = U^2 / 2g - 5 U^2 / 9g

=> ∆ H = - U ^ 2 / 18 g

Decrease in Percentage of Height :

=> [ ∆ H / H ] × 100%

= > [ { - U ^ 2 / 18 g } / { U^2 / 2g } ] × 100 %

=> [ 1 / 9 ] × 100 %

=> 100 / 9 %

=> 11 { 1 / 9 } %

Answer :

The maximum height will be decreased by 11 { 1 / 9 } %.