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Atoms And Molecules

Question
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A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Find when and where the two stones meet?

Solution

Suppose the two stones meet at a height x from the ground, after time t from the start.

For space the space downward space motion space of space stone space straight A colon straight u space equals space 0 space straight m divided by straight s comma space straight g space equals space minus 10 space straight m divided by straight s squared comma space straight s space equals space left parenthesis negative 100 minus straight x right parenthesis space As comma space straight s space equals space ut space plus space 1 half gt squared therefore space minus left parenthesis 100 minus straight x right parenthesis space equals space 0 space minus space space 1 half cross times 10 cross times straight t squared space space space space... space left parenthesis 1 right parenthesis For space upward space motion space of space stone space straight B colon straight u space equals space plus 25 space straight m divided by straight s comma space straight g space equals space minus 10 straight m divided by straight s squared comma space straight s space equals space plus straight x space straight m Using space the space formula comma space space straight s space equals space ut space plus space 1 half gt squared therefore space plus straight x space equals space 25 space straight t space minus space 1 half cross times 10 straight t squared space space space space space space space space space space space space space space space space space... thin space left parenthesis 2 right parenthesis Now comma space subtracting space left parenthesis 1 right parenthesis space from space left parenthesis 2 right parenthesis comma space we space get space space space space space space 100 space equals space 25 space straight t rightwards double arrow space space straight t space equals space 4 space sec From space equation space left parenthesis 2 right parenthesis comma space we space have straight x space equals space 25 cross times 4 space minus 1 half cross times 10 cross times left parenthesis 4 right parenthesis squared space space space equals 100 space minus space 80 space space space equals space 20 space straight m
Hence, the two stones meet after 4 sec at a height of 20 m from the ground or 80 m from the top.

 

Some More Questions From Atoms And Molecules Chapter

Convert into mole

(a) 12 gm of oxygen gas

(b) 20 gm of water

(c) 22 gm of carbon dioxide.

What is the mass of?

(a) 0.2 mole oxygen atoms.

(b) 0.5 mole of water molecules.

Calculate the number of molecules of sulphur (S8) present in 16 gm of solid sulphur.

Calculate the number of aluminium ions present in 0.56 gm of aluminium oxide.

Explain law of conservation of mass.

50 g of 10% lead nitrate is mixed with 50 g of 10% sodium chloride in a closed vessel. After the reaction has taken place, it was found that 6.83 g of lead chloride was precipitated. Besides, the reaction mixture contained 90 g water and sodium nitrate. Calculate the amount of sodium nitrate formed.

Name and explain two important laws of chemical combination ?

What are the postulates of Dalton’s atomic theory of matter?

Hydrogen and oxygen combine in two different ways to produce water and hydrogen peroxide. Which of Dalton’s law does this observation confirm? Explain.

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