Question

A stone is thrown in a vertically upward direction with a velocity of 5ms if the acceleration of the stone during it's motion is 10ms in the upward direction what will be the height attained by the stone and how much time it will take to reach there​​

Answer 1

Given

a=-10m/s²

u=5m/s

v=0

v²-u²=2as

0-25=2{-10}s

-25=-20s

s=25/20=5/4m

s=ut+1/2at²

5/4=5t+1/2{-10}t²

5t-5t²=5/4

5{t-t²}=5/4

t-t²=1/4

t-t²-1/4=0

-t²+t-1/4=0

-t²+1/2t+1/2t-1/4=0

-t{t-1/2}+1/2{t-1/2}=0

(-t+1/2)(t-1/2)=0

t=1/2s

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Answer 2

Question :-

A stone is thrown vertically upward with a velocity of 5 m/s . If the acceleration of the stone during its motion is - 10 m/s² in the upward direction . Find the height attained by the stone and how much time it will take to reach it .

Answer :-

Given :-

A stone is thrown vertically upward with a velocity of 5 m/s . If the acceleration of the stone during its motion is - 10 m/s² in the upward direction

Required to find :-

• The height attained by the stone ?

• Time taken by the stone to reach the height ?

Equations used :-

➪ v² - u² = 2as

➪ s = ut + ½ at²

Solution :-

Given data :-

A stone is thrown vertically upward with a velocity of 5 m/s . If the acceleration of the stone during its motion is - 10 m/s² in the upward direction

we need to find the height attained by the stone and the time taken by the stone to reach the height .

From the given data we can conclude that ;

• Initial velocity of the stone ( u ) = 5 m/s

• Acceleration of the stone ( a ) = - 10 m/s

• Final velocity of the stone ( v ) = 0 m/s

Using the equation of motion ; i.e.

➜ v² - u² = 2as

➜ ( 0 ) - ( 5 )² = 2 x - 10 x s

➜ 0 - 5 = 2 x - 10s

➜ - 5 = - 20s

➜ Taking - ( minus ) common on both sides

➜ - ( 5 ) = - ( 20s )

➜ 5 = 20s

➜ 20s = 5

➜ s = 5/20

➜ s = 0.5/2

➜ s = 0.25 meters

Hence,

• Displacement of the stone ( s ) = 0.25 meters

Now, using the next equation of motion ; i.e.

➜ s = ut + ½ at²

➜ 0.25 = 5 x t + ½ x - 10 x t²

➜ 0.25 = 5t + ( - 5 ) X t²

➜ 25/100 = 5t + ( - 5t² )

➜ 25/100 = 5t - 5t²

➜ 5t² - 5t + 25/100 = 0

➜ 5 ( t² - t + 5/20 ) = 0

➜ t² - t + 5/20 = 0

➜ t² - t + 0.25 = 0

➜ t² - 0.5t - 0.5t + 0.25 = 0

➜ t ( t - 0.5 ) - 0.5( t - 0.5 ) = 0

➜ ( t - 0.5 ) ( t - 0.5 ) = 0

This implies,

➜ ( t - 0.5 )² = 0

➜ t - 0.5 = √0

➜ t - 0.5 = 0

➜ t = 0.5 seconds

Hence,

• Time taken by the stone ( t ) = 0.5 seconds

Therefore ,

✮ The height attained by the stone is 0.25 meters

✮ The time taken by the stone to reach the height is 0.5 meters