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M1 help

2

Hi.

Could someone please help me with the following M1 vector question? I would really appreciate it as I am really stuck.

At time t = 0, two ice skaters John (J) and Norma (N) have position vectors 40j metres and 20i metres relative to an origin O at the centre of an ice rink, where i and j are unit vectors perpendicular to each other. John has constant velocity 5i m/s and Norma has constant velocity (3i + 4j) m/s.

(a) Show that the skaters will collide an find the time at which the collison takes place.

I got that t is equal to 10 seconds and this is the correct answer in the back of the textbook.

(b) On another occasion, John has position vector 40j metres. He wishes to skate in a straight line to the point with position vector 30i metres. Given that is speed is constant at 5 m/s, find his velocity.

I drew a diagram and wrote down that 30i = 40j + vt, but I do not know where to go from here.

Thank you.

Cathy

Reply 1

Font

CathyLou

Hi.

Could someone please help me with the following M1 vector question? I would really appreciate it as I am really stuck.

At time t = 0, two ice skaters John (J) and Norma (N) have position vectors 40j metres and 20i metres relative to an origin O at the centre of an ice rink, where i and j are unit vectors perpendicular to each other. John has constant velocity 5i m/s and Norma has constant velocity (3i + 4j) m/s.

(a) Show that the skaters will collide an find the time at which the collison takes place.

I got that t is equal to 10 seconds and this is the correct answer in the back of the textbook.

(b) On another occasion, John has position vector 40j metres. He wishes to skate in a straight line to the point with position vector 30i metres. Given that is speed is constant at 5 m/s, find his velocity.

I drew a diagram and wrote down that 30i = 40j + vt, but I do not know where to go from here.

(3i -4j) m/s
Thank you.

Cathy

(3i -4j) m/s

Reply 2

CathyLou

OP

2

Thanks for your help.

I have figured out how to do it now.

Cathy

Reply 3

CathyLou

OP

2

Hi.

Could someone please tell me how to do the following vector question as I am really stuck.

8.

(a) Given that the vector ai + 3j is parallel to the vector 2i + 12j find a.

(b) Given that the vector 3i + bj is parallel to 12i - 20j find b.

(c) Given that the vector 7i + cj has magnitude 25 find the two possible values of c.

Any help would be really appreciated.

Thank you.

Cathy

Reply 4

Square

13

If x and y are two vectors, and you are told the two are parallel, then x=ay. ie one is a multiple of the other.

For part c) remember the formula for the magnitude of a vector:

Say Y=ai +bj - it follows that the magnitude of Y (denoted as |Y|) =

\displaystyle \sqrt{a^2+b^2}

Post back if you are still having problems.

Reply 5

SunGod87

7

If the vector ai + bj is parallel to ci + dj then

ai + bj = k(ci + dj)

Can you see how to work out k, then how to apply it to work out the unknown value?

The magnitude of a vector ai + bj = (a^2 + b^2)^(1/2)

Reply 6

CathyLou

OP

2

Thanks to both of you for your help.

I have got the answers now. :smile:

Cathy

Reply 7

CathyLou

OP

2

I am now stuck on this question.

Could someone please help? I would really appreciate any advice.

The position vector r of a particle P at time t is given by r = t^2i + (12 - t)j. Find the value of t when:

(a) r is parallel to the vector i

(b) r is parallel to the vector i + j.

Thank you.

Cathy

Reply 8

SunGod87

7

For a you want to know when the j component = 0
For b you want to know when the i component = the j component.

Right?

Reply 9

CathyLou

OP

2

SunGod87

For a you want to know when the j component = 0
For b you want to know when the i component = the j component.

Right?

I get it now.

Thanks again for your help.

Cathy

Reply 10

CathyLou

OP

2

Okay, last question that I need to do. Could someone please help?

At 11:00 hours the position vector of an aircraft relative to an airport O is (200i + 30j) km, i and j being unit vectors due east and due north respectively. The velocity of the aircraft is (180i - 120j) km/h. Find:

(a) the time when the aircraft is due east of the airport O.

Thank you.

Cathy

M1 help

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