Question

A stone loses 1/10th of its velocity on passing through a sand bag of length x. For its velocity to be made zero, how many more similar bags are to be placed on its path?

Answer 1

Answer:

5 more bags are to be placed

Explanation:

A stone loses 1/10th of its velocity on passing through a sand bag of length x. For its velocity to be made zero, how many more similar bags are to be placed on its path?

Let say initial Velocity of stone = V

Distance traveled = x  ( length of Sand Bag)

Final Velocity after sandbag = V - (1/10)V = (9/10)V

Using V² - U² = 2as

((9/10)V)² - V²  = 2ax

=> (-19/100)V² = 2ax

Final Velocity to be zero  & ,Let say n bags to be put

0² - V² = 2a (nx)

=> -V² = n (2ax)

=> -V² = n (-19/100)V²

=>  1 = n(19/100)

=>n = 100/19

=> n = 5.26

Total Six bags will be required

=> 5 more bags are to be placed

Answer 2

Let initial velocity of stone is u , the stone loses 1/10th of its velocity on passing through a sand bag of length x.

then, velocity of the stone after penetrating a sand bag , v = u - u/10 = 9u/10

using formula, v² = u² + 2as

here, v = 9u/10, s = x

then, (9u/10)² = u² + 2ax

or, 81u²/100 - u² = 2ax

or, -19u²/100 = 2ax

or, a = -19u²/200x .....(1)

Let after penetrating n sand bags velocity of the stone becomes zero.

so, final velocity of the stone , v = 0,

Initial velocity of the stone is u

and a = -19u²/200x [ from equation (1}]

now using formula, v² = u² + 2as

here, s = nx

so, 0 = u² + 2(-19u²/200x) × nx

or, u² = 19u²/100x × nx

or, 1 = 19n/100

or, n = 100/19 = 5.26

so, total 6 number of sand bags will require

hence, 5 more sand bags are placed to be placed on its path.