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Motion In Straight Line

Question
CBSEENPH11019924
Wired Faculty App

A ball is dropped from a height of 90 m on a floor. At each collision with the floor,  the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

Solution
Height space from space which space the space ball space is space dropped comma space straight s space equals space 90 space straight m Initial space velocity space of space the space ball comma space straight u space equals space 0 space straight m divided by straight s Acceleration comma space straight a space equals space 9.8 space straight m divided by straight s squared space Final space velocity space of space the space ball space equals space straight v space Using space second space equation space of space motion comma space Time left parenthesis straight t right parenthesis space taken space by space the space ball space to space hit space the space ground space is comma space straight s space equals space ut space plus space 1 half at squared space 90 space equals space 0 space plus space space 1 half cross times 9.8 straight t squared space straight t space equals space square root of 18.38 end root space equals space 4.29 space sec Using space first space equation space of space motion comma space Final space velcoity comma space straight v space equals space straight u space plus space at space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0 space plus space 9.8 space cross times space 4.29 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 42.04 space straight m divided by straight s space Rebound space velocity space of space the space ball comma space straight u subscript straight r space equals space fraction numerator 9 straight v space over denominator 10 end fraction space equals space fraction numerator 9 cross times 42.04 over denominator 10 end fraction space equals space 37.84 space straight m divided by straight s Time left parenthesis straight t right parenthesis space taken space by space the space ball space to space reach space straight a space maximum space height space is comma space Using space first space equation space of space motion comma space straight v space equals space straight u subscript straight r space plus space at apostrophe space 0 space equals space 37.84 space plus space left parenthesis – space 9.8 right parenthesis space straight t apostrophe straight t apostrophe space equals space minus 37.84 space divided by space minus 9.8 space equals space 3.86 space straight s space Total space time space taken space by space the space ball space equals space straight t space plus space straight t apostrophe space equals space 4.29 space plus space 3.86 space equals space 8.15 space straight s Since comma space time space of space ascent space equals space time space of space descent comma space Time space taken space by space the space ball space to space rebound space from space the space floor space equals space 3.86 space straight s Velocity space with space which space the space ball space rebounds from space the space floor space equals space 9 cross times fraction numerator 37.84 over denominator 10 end fraction equals 34.05 space straight m divided by straight s Total space time space taken space by space the space ball space from space second space rebound space equals 8.15 space plus space 3.86 space equals space 12.01 space straight s 
Speed-time graph for the ball is as shown below: 


Some More Questions From Motion in Straight Line Chapter

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

 A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: 

(a) A kite flying in the sky.

(b) The earth revolving around the sun. 

(c) A train moving along the equator of the earth in clockwise direction. 

(d) Accelerated motion of a particle in a straight line.

Define distance.

Define displacement.

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