Question

A stone falls freely from rest from height h and it travels a distance 9h/25 in the last second. the value of h site:in.answers..com

Answer 1

Answer: 122.5 m

Given, distance travelled in last second = 9h/25

We know that,  

                       $h\quad =\quad \frac { 1 }{ 2 } \quad \times \quad g\quad \times \quad { t }^{ 2 }\quad ......(1)$

Hence, distance covered for the remaining seconds i.e.,

                       $\left( t-1 \right) seconds\quad =\quad h\quad -\quad \frac { 9h }{ 25 } \quad =\quad \frac { 16h }{ 25 }$

Height reached in (t-1) seconds

                       $=\quad \frac { 1 }{ 2 } \quad \times \quad g\quad \times \quad { \left( t-1 \right)  }^{ 2 }\quad \\=\quad \frac { 16h }{ 25 }$

On equating,  

                       $g\quad \times \quad { (t\quad -\quad 1) }^{ 2 }\quad =\quad \frac { 32h }{ 25 }$

substituting the value h,

                       $g\quad \times \quad { (t\quad -\quad 1) }^{ 2 }\quad =\quad \frac { 32\quad \times \quad g\quad \times \quad { t }^{ 2 } }{ 2\quad \times \quad 25 }$

                       ${ (t\quad -\quad 1) }^{ 2 }\quad =\quad \frac { 16\quad \times \quad { t }^{ 2 } }{ 25 }$

                       ${ t }^{ 2 }\quad +\quad 1\quad -\quad 2t\quad =\quad \frac { 16{ t }^{ 2 } }{ 25 }$

                       $25{ t }^{ 2 }\quad +\quad 25\quad -\quad 50t\quad =\quad 16{ t }^{ 2 }$

                       $25{ t }^{ 2 }\quad -\quad 16{ t }^{ 2 }\quad +\quad 25\quad -\quad 50t\quad =\quad 0$

                       $9{ t }^{ 2 }\quad +\quad 25\quad -\quad 50t\quad =\quad 0$

On factorization we get, t = 5 or t = 5/9

Second option is not possible since they have given as the last second, which means it is a whole number.

Substituting

                       $t\quad =\quad 5\quad and\quad g\quad =\quad 9.8\quad m/{ s }^{ 2 }\quad in\quad equation\quad (1)$

                       $h\quad =\quad \frac { 1 }{ 2 } \quad \times \quad 9.8\quad \times \quad 25\quad =\quad 122.5\quad meters$

Answer 2

Explanation:

Please follow me

Hope it helps you