Miscellaneous Exercise 21
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Transcript of Miscellaneous Exercise 21
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Dr Lee Chu Keong (http://ascklee.org/)
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Solutions to Miscellaneous Exercise 21 (Ho Soo Thong & Khor Nyak Hiong’s Panpac Additional Mathematics)
Solved by: Dr Lee Chu Keong ([email protected])
![Page 2: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/2.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
1
Miscellaneous Exercise 21 Question 1(a)
( )
( )( )
The particle is instantaneously at rest at .
( )
Question 1(b)
( )
(√ )(√ )
√
The particle is next at O at √ :
(√ )
( )
Question 1(c)
( ) ( )
( ) ( )
Question 1(d)
Summary:
,
![Page 3: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/3.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
2
,
,
( )
Question 2(a)
When ,
When :
( )
Question 2(b)
( )( )
( ) ( )
( )
Question 3(a)
( )
( ( ) )
![Page 4: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/4.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
3
Question 3(b)
( )
( )
( )
( )
Question 3(c)
( )
( )
( )
( )
( )
( )
( )( )
![Page 5: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/5.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
4
At , :
( ) ( )
(
)
Question 4(a)
( )
“a particle starts from rest” which means that at , :
( )
When :
( )
Question 4(b)
At , :
( ) ( )
( ) ( )
Question 5(a)
When :
![Page 6: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/6.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
5
( )
( )
Question 5(b)
When , :
( )
( )
Question 6(a)
( )( )
At , the particle comes to instantaneous rest at A
At , the particle comes to instantaneous rest at B
“t seconds after passing though O” means that at , :
( )
( ) ( )
Question 6(b)
( )
( ) ( )
![Page 7: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/7.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
6
( )
( ) ( )
Question 6(c)
( )
( ) ( )
Question 7
When , :
When , :
When , :
( ) ( )
![Page 8: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/8.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
7
At :
( )
√
At √ :
(√ )
(√ )
( √ ) √
√ √
√
Summary:
At ,
At √ , √
At ,
√ √ √ Question 8(a)
![Page 9: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/9.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
8
Question 8(b)
( )
When , :
( )
(
)
Question 9(a)
( )
( )
( )
Question 9(b)
( )
![Page 10: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/10.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
9
Question 9(c)
( )
Question 9(d)
( )
( )
( )
when
( )
Question 10(a) ( )
Question 10(b)
At :
( )
When , :
( ) ( )
When :
( )
Question 10(c)
![Page 11: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/11.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
10
The plot of below shows that the particle will never return to O.
Question 11(a)
At :
Question 11(b)
(
)
1 2 3 4t
10
20
30
40
50
s
![Page 12: Miscellaneous Exercise 21](https://reader034.fdocuments.us/reader034/viewer/2022042503/55cf9267550346f57b96341e/html5/thumbnails/12.jpg)
Dr Lee Chu Keong (http://ascklee.org/)
11
( )
( )
Question 11(c)
(
)
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