Additional Mathematics; Post some challenging questions here

[Haris Bin Zahid]

I'm unable to solve a relative velocity question. Have a try at it and post your solution here.
Q. A footballer C runs at a speed of 5 m/s, with the ball close to his feet, in a straight line towards the point (0,0). At the instant when he passes through the point (15,20), another footballer D starts to run in a straight line, at 8.5 m/s, from the point (-27,20) at an angle θ as shown in the diagram. Given that D intercepts the ball, and that the given coordinates are in metres, find
(a) the value of θ,
(b) the velocity of D relative to C,
(c) the time taken by D to intercept the ball.

 

[mohdumar]

I'm unable to solve a relative velocity question. Have a try at it and post your solution here.
Q. A footballer C runs at a speed of 5 m/s, with the ball close to his feet, in a straight line towards the point (0,0). At the instant when he passes through the point (15,20), another footballer D starts to run in a straight line, at 8.5 m/s, from the point (-27,20) at an angle θ as shown in the diagram. Given that D intercepts the aball, and that the given coordinates are in metres, find
(a) the value of θ,
(b) the velocity of D relative to C,
(c) the time taken by D to intercept the ball.

Where is the diagram?

 

[Haris Bin Zahid]

Where is the diagram?

Uploaded just now.
I'm only getting the first part of the question right.

 

[mohdumar]

Uploaded just now.
I'm only getting the first part of the question right.

Can u post final answers?

 

[Haris Bin Zahid]

Can u post final answers?

(a) 28.1 degrees
(b) 9.18 m/s
(c) 3.44 s

 

[mohdumar]

 

[Haris Bin Zahid]

View attachment 27877

Yeah I know how to work out the first part. Are you getting the answers to the subsequent parts right? Because my answers are 10.4 m/s and 4 s, which do not match with the correct answers.
Btw thanks for taking interest.

 

[Haris Bin Zahid]

Ok here's another one:
The position vectors of points A and B, relative to an origin O, are 2i + 4j and 6i + 10j respectively. The position vector of C, relative to O, is ki + 25j, where k is a positive constant.
(i) Find the value of k for which the length of BC is 25 units.

I know that the value of k is 26. But why do we reject the other solution i.e. -14 ?

 

[mohdumar]

Yeah I know how to work out the first part. Are you getting the answers to the subsequent parts right? Because my answers are 10.4 m/s and 4 s, which do not match with the correct answers.
Btw thanks for taking interest.

yeah me too getting same answers as urs!!!

 

[mohdumar]

Ok here's another one:
The position vectors of points A and B, relative to an origin O, are 2i + 4j and 6i + 10j respectively. The position vector of C, relative to O, is ki + 25j, where k is a positive constant.
(i) Find the value of k for which the length of BC is 25 units.

I know that the value of k is 26. But why do we reject the other solution i.e. -14 ?

the question says "where k is a positive constant."

 

[Saad Mughal]

(a) 28.1 degrees
(b) 9.18 m/s
(c) 3.44 s

I'm getting the same answers as you. 28.1, 10.5 m/s and 4 s.

 

[mohdumar]

I'm getting the same answers as you. 28.1, 10.5 m/s and 4 s.

Dnt worry many at times books answers can be incorrect.

 

[Saad Mughal]

Dnt worry many at times books answers can be incorrect.

I've found many errors in Classified as well.

 

[Haris Bin Zahid]

the question says "where k is a positive constant."

I don't know when I'll get rid of this disease of hastily reading the question. I wish it doesn't cost me in the exam.

 

[Saad Mughal]

I don't know when I'll get rid of this disease of hastily reading the question. I wish it doesn't cost me in the exam.

It already has cost me 2 marks in the maths exam.

 

[Haris Bin Zahid]

Dnt worry many at times books answers can be incorrect.

yeah me too getting same answers as urs!!!

I'm getting the same answers as you. 28.1, 10.5 m/s and 4 s.

Yeah....we three cannot be wrong. Thanks a lot.