Question

A ballon is rising up at 30m/sec .and a stone is released from it when it is at a height 80m above ground . find the time after which stone will hit the ground.

​

Answer 1

Question :

A balloon is rising up at 30m/s and A stone is released from it when it is at a height 80m above ground. Find the time after which stone will hit the ground.

AnsWer :

After 8 second.

Given value :

$\: \: \tt \vec{a} = - g \: \: \: \: \: \: \: \leadsto - 10. \\ \: \: \tt \vec{u} = 30 \: s. \\ \: \: \tt \vec{s} = 80 \: m.$

Formula Use :

$\tt \: \: \vec{s} = ut + \frac{1}{2} a {t}^{2}$

Solution :

$\tt \leadsto - 80 = 30t + \frac{1}{2} ( - 10) \times {t}^{2} .$

$\tt \leadsto - 80 = 30t - 5 {t}^{2} .$

$\tt \leadsto - 80 = - 5 {t}^{2} + 30t .$

$\tt \leadsto 0 = - 5 {t}^{2} + 30t + 80 .$

$\tt \leadsto 0 = 5 {t}^{2} - 30t - 80.$

$\tt\leadsto0 = {t}^{2} - 6t - 16.$

$\tt\leadsto0 = {t}^{2} - 8t + 2t - 16.$

$\tt\leadsto0 = t(t - 8) + 2(t - 8).$

$\tt\leadsto0 = (t - 8)(t + 2).$

$\tt\leadsto0 = (t + 2) \\ \leadsto\tt t = - 2.$

And,

$\tt\leadsto0 = (t - 8) \\ \tt \leadsto t = 8.$

Therefore,after 8 second stone hit the ground.

Answer 2

Question :

A balloon is rising up at 30m/s and A stone is released from it when it is at a height 80m above ground. Find the time after which stone will hit the ground.

AnsWer :

After 8 second.

Given value :

$\: \: \tt \vec{a} = - g \: \: \: \: \: \: \: \leadsto - 10. \\ \: \: \tt \vec{u} = 30 \: s. \\ \: \: \tt \vec{s} = 80 \: m.$

Formula Use :

$\tt \: \: \vec{s} = ut + \frac{1}{2} a {t}^{2}$

Solution :

$\tt \leadsto - 80 = 30t + \frac{1}{2} ( - 10) \times {t}^{2} .$

$\tt \leadsto - 80 = 30t - 5 {t}^{2} .$

$\tt \leadsto - 80 = - 5 {t}^{2} + 30t .$

$\tt \leadsto 0 = - 5 {t}^{2} + 30t + 80 .$

$\tt \leadsto 0 = 5 {t}^{2} - 30t - 80.$

$\tt\leadsto0 = {t}^{2} - 6t - 16.$

$\tt\leadsto0 = {t}^{2} - 8t + 2t - 16.$

$\tt\leadsto0 = t(t - 8) + 2(t - 8).$

$\tt\leadsto0 = (t - 8)(t + 2).$

$\tt\leadsto0 = (t + 2) \\ \leadsto\tt t = - 2.$

And,

$\tt\leadsto0 = (t - 8) \\ \tt \leadsto t = 8.$

Therefore,after 8 second stone hit the ground.