Grade 11Mechanics

A stone is thrown vertically upwards. When stone is at half height of its maximum height, it`s speed is 10 ,then maximum height attained by stone is

Shubham

9 Years agoGrade 11

1 Answer

Vaibhav Singh

9 Years ago

This is a tricky one if you go to solve it by kinematic formulae.whereas it can be easily solved by energy conservation.

Let maximum height be h therefore half height will be h/2.

Let the initial point be the reference point, therefore potential energy, mgh=0 and kinetic energy KE = 1/2mu²
Potential energy at half height, PE = mgh/2 and KE = 1/2m(10)²
PEat max height, PE = mgh and KE = 0.
Now applying energy conservation

PE + KE (at initial) = PE + KE (at half height)

=> 1/2mu² +0 = 1/2m(100) +mgh/2

=> 1/2u² = 50 + 5h ( g = 10m/s²)

=> u² = 100 +10h -------------(i)

Now at heighest point, mgh + 0 = 1/2mu²

=> 10h =1/2u²

=> u² = 20h -----------(ii)

From (i) and (ii)

20h = 100 + 10h

=> h = 10 m

Therefore max height is 10 m.

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A stone is thrown vertically upwards. When stone is at half height of its maximum height, it`s speed is 10 ,then maximum height attained by stone is

Shubham

1 Answer

Vaibhav Singh

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