Dr Lee Chu Keong (http://ascklee.org/)

0

Solutions to Exercise 21.1 (Ho Soo Thong & Khor Nyak Hiongs Panpac Additional Mathematics)

Solved by: Dr Lee Chu Keong (ascklee@gmail.com)

http://ascklee.org/CV/CV.pdf

Dr Lee Chu Keong (http://ascklee.org/)

1

Exercise 21.1 Question 1(a)

( )

When , ( ) ( )

Question 1(b)

( )

( )( )

Question 1(c)

When ,

( )

Question 2(a)

( )

( )( )

It comes to rest at .

( )

Dr Lee Chu Keong (http://ascklee.org/)

2

Question 2(b)

( )

( )( )

Question 2(c)

( )

( )

( )

Question 3(a)

( )

( )( )

P comes to rest at and .

( ) ( )

Question 3(b) ( ) ( )

( )

Dr Lee Chu Keong (http://ascklee.org/)

3

Question 3(c)

( ) ( )

Question 4(a)

At : ( )

Question 4(b)

At the maximum height, the velocity is zero:

The maximum height happens at :

( ) ( )

Question 4(c)

Time of flight is the time taken to get back to the ground ( ) again:

( )

Dr Lee Chu Keong (http://ascklee.org/)

4

Question 5(a)

( )

( )( )

At , the velocity is instantaneously zero:

( ) ( ) ( )

At , the velocity is instantaneously zero:

( ) ( ) ( )

Question 5(b)

acceleration has a magnitude of means that acceleration can be either

or :

Question 5(c) At :

At : ( ) ( ) ( )

Dr Lee Chu Keong (http://ascklee.org/)

5

At : ( ) ( ) ( )

( )

Question 6(a)

When , :

( )( )

When , the particle is at rest ( )

The displacement at this instant:

( )

( ) ( )

Question 6(b)

( )

( ) ( )

Summary:

Dr Lee Chu Keong (http://ascklee.org/)

6

,

,

,

Question 7(a)

Question 7(b)

When , :

Question 7(c)

( )( )

when

when the particle passes through O again implies that :

( )

( )( )

Question 8(a)

instantaneously at rest implies that :

Dr Lee Chu Keong (http://ascklee.org/)

7

Question 8(b)

t is the time in seconds, measured from the start of the motion implies that when

, :

(

)

Question 18(c)

Summary:

,

,

,

( )

Question 9(a)

( )

When ,

( )

Dr Lee Chu Keong (http://ascklee.org/)

8

Question 9(b)

When , :

( ) ( )

( )

Question 10(a)

At , :

Acceleration as it passes O is acceleration at :

( )

Question 10(b)

When , :

At :

At : ( )

( )

Dr Lee Chu Keong (http://ascklee.org/)

9

Question 11(a)

The particle starts from rest, which means that at , :

( )

The time to reach A is 4 seconds.

Question 11(b)

t is the time in seconds after leaving O implies that at , :

( )

( )

Question 11(c)

This is a quadratic equation. a is negative, which means that the graph is frowning.

Re-writing the equation as:

( )

We see that the graph has a maximum at .

( )( )

Question 12(a)

At , :

Dr Lee Chu Keong (http://ascklee.org/)

10

At :

( ) ( )

Question 12(b)

( )( )

Question 12(c)

t seconds after passing O implies at , :

( ) ( ) ( )

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